AP 10th Class Maths Bits Chapter 11 Trigonometry with Answers

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AP State Syllabus 10th Class Maths Bits 11th Lesson Trigonometry with Answers

Question 1.
If cosec θ + cot θ = 2, then cos θ =
A) \(\frac{3}{5}\)
B) \(\frac{4}{5}\)
C) \(\frac{5}{3}\)
D) \(\frac{6}{5}\)
Answer:
A) \(\frac{3}{5}\)

Question 2.
If 4 cos² θ – 3 = 0, then sin θ =…………………….
A) \(\frac{1}{2}\)
B) –\(\frac{1}{2}\)
C) \(\frac{1}{\sqrt{2}}\)
D) \(\frac{\sqrt{3}}{2}\)
Answer:
A) \(\frac{1}{2}\)

Question 3.
If cos (A + B) = 0, cos B = \(\frac{\sqrt{3}}{2}\) then A =
A) 15°
B) 60°
C) 30°
D) 45°
Answer:
B) 60°

Question 4.
If sec θ + tan θ = \(\frac{1}{3}\), then sec θ – tan θ = …………………
A) 3
B) \(\frac{1}{3}\)
C) 1
D) 0
Answer:
A) 3

Question 5.
If sin x = \(\frac{5}{7}\) , then cosec x = …………………….
A) \(\frac{5}{7}\)
B) \(\frac{7}{5}\)
C) \(\frac{2}{5}\)
D) \(\frac{2}{7}\)
Answer:
B) \(\frac{7}{5}\)

Question 6.
Given ∠A = 75°, ∠B = 30°, then tan (A-B) = …………………
A) √3
B) \(\frac{1}{\sqrt{3}}\)
C) 1
D) \(\frac{1}{\sqrt{2}}\)
Answer:
C) 1

Question 7.
Which one of the following is NOT defined?
A) sin 90°
B) cos 0°
C) sec 90°
D) cos 90°
Answer:
C) sec 90°

Question 8.
………………….
A) sin A
B) \(\sqrt{\sin A}\)
C) sin²A
D) sin⁴A
Answer:
C) sin²A

Question 9.
tan 36°. tan 54° + sin 30° = ………………..
A) \(\frac{3}{2}\)
B) \(\frac{1}{2}\)
C) 2
D) \(\frac{2}{3}\)
Answer:
A) \(\frac{3}{2}\)

Question 10.
If sin A = \(\frac{24}{25}\), then sec A = ………………………
A) \(\frac{7}{25}\)
B) \(\frac{25}{7}\)
C) \(\frac{24}{7}\)
D) \(\frac{7}{24}\)
Answer:
B) \(\frac{25}{7}\)

Question 11.
Values of sin 30°. sin 90°. sec 60° are in …………………
A) A.P.
B) G.P.
C) a
D) (A)or(C)
Answer:
B) G.P.

Question 12.
From the figure : Sin A =

A) \(\frac{\mathrm{AC}}{\mathrm{BC}}\)
B) \(\frac{\mathrm{BC}}{\mathrm{AC}}\)
C) \(\frac{\mathrm{BC}}{\mathrm{AB}}\)
D) \(\frac{\mathrm{AC}}{\mathrm{AB}}\)
Answer:
B) \(\frac{\mathrm{BC}}{\mathrm{AC}}\)

Question 13.
The value of tan θ in terms of sinθ is
A) \(\frac{\sin \theta}{1-\sin ^{2} \theta}\)
B) \(\frac{\sqrt{\sin ^{2} \theta-1}}{\sin \theta}\)
C) \(\frac{\sin \theta}{\sqrt{1-\sin ^{2} \theta}}\)
D) \(\frac{\sqrt{1-\sin ^{2} \theta}}{\sin \theta}\)
Answer:
C) \(\frac{\sin \theta}{\sqrt{1-\sin ^{2} \theta}}\)

Question 14.
If cosec θ = 2 and cot θ = \(\sqrt{3 \mathbf{p}}\) where ‘θ’ is an acute angle, then p =
A) 2
B) 1
C) \(\frac{1}{2}\)
D) √3
Answer:
B) 1

Question 15.
If sec θ = 3K and tan θ = \(\frac{3}{K}\), then K² – \(\frac{\mathbf{1}}{\mathbf{K}^{2}}\) =
A) 9
B) \(\frac{1}{9}\)
C) 3
D) \(\frac{1}{3}\)
Answer:
B) \(\frac{1}{9}\)

Question 16.
tan θ is not defined when ‘θ’ is
A) 0°
B) 30°
C) 60°
D) 90°
Answer:
D) 90°

Question 17.
It tan θ = \(\frac{1}{\sqrt{3}}\), then 7 sin²θ + 3 cos²θ =
A) \(\frac{16}{4}\)
B) \(\frac{7}{4}\)
C) \(\frac{9}{4}\)
D) 1
Answer:
A) \(\frac{16}{4}\)

Question 18.
If cos 2θ = sin 4θ, here 2θ, 4θ are acute angles, then the value of ‘θ’ =
A) 60°
B) 30°
C) 45°
D) 15°
Answer:
D) 15°

Question 19.
Values of cos²0° + cos² 60° is
A) \(\frac{5}{4}\)
B) \(\frac{2}{\sqrt{3}}\)
C) \(\frac{1}{\sqrt{2}}\)
D) \(\frac{\sqrt{3}}{2}\)
Answer:
A) \(\frac{5}{4}\)

Question 20.
If Sin A = Cos B then A + B = ……………………..
A) 60°
B) 90°
C) 45°
D) 120°
Answer:
B) 90°

Question 21.
If 5 tan α = 4, then \(\frac{5 \sin \alpha-3 \cos \alpha}{5 \sin \alpha+2 \cos \alpha}\) = ………………….
A) \(\frac{1}{7}\)
B) \(\frac{1}{6}\)
C) \(\frac{2}{5}\)
D) \(\frac{3}{7}\))
Answer:
B) \(\frac{1}{6}\)

Question 22.
\(\sqrt{1+\sin ^{2} \theta+\cos ^{2} \theta}\) = …………………
A) 1
B) 2
C) \(\sqrt{21}\)
D) √2
Answer:

Question 23.
tan 2A = 1 then A = …………………..
A) 45.5
B) 60.5
C) 22.5
D) 30.5
Answer:
C) 22.5

Question 24.
If x = a secθ cosΦ, y = b secθ sinΦ. z = c tan θ, then \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = ………………….
A) \(\frac{z^{2}}{c^{2}}\)
B) 1 – \(\frac{z^{2}}{c^{2}}\)
C) \(\frac{z^{2}}{c^{2}}\) – 1
D) 1 + \(\frac{z^{2}}{c^{2}}\)
Answer:
D) 1 + \(\frac{z^{2}}{c^{2}}\)

Question 25.
If 7sin²θ + 3 cos²θ = 5, then tan θ = ……………………
A) √3
B) \(\frac{1}{\sqrt{3}}\)
C) 1
D) 0
Answer:
C) 1

Question 26.
If sinθ + sin²θ = 1, then cos²θ + cos⁴θ = ……………..
A) -1
B) 1
C) 0
D) None of these
Answer:
B) 1

Question 27.
If cotθ + cosecθ = 5, then cosθ = ………………..
A) \(\frac{12}{13}\)
B) \(\frac{26}{24}\)
C) \(\frac{5}{13}\)
D) \(\frac{13}{12}\)
Answer:
A) \(\frac{12}{13}\)

Question 28.
\(\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}\) = ………………
A) cos θ – sin θ
B) tan θ – cot θ
C) cos θ – sin θ
D) tan θ + cot θ
Answer:
A) cos θ – sin θ

Question 29.
If tanθ = \(\frac{7}{8}\), then the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\) ……………….
A) \(\frac{64}{49}\)
B) \(\frac{49}{64}\)
C) \(\frac{8}{7}\)
D) \(\frac{7}{8}\)
Answer:
A) \(\frac{64}{49}\)

Question 30.
If cosecθ + cotθ = P, then value of cosθ = ……………………
A) \(\frac{1-P^{2}}{1+P^{2}}\)
B) \(\frac{1-\mathrm{P}^{2}}{2 \mathrm{P}}\)
C) \(\frac{2 P}{1+P^{2}}\)
D) \(\frac{2 \mathrm{P}}{1-\mathrm{P}^{2}}\)
Answer:
A) \(\frac{1-P^{2}}{1+P^{2}}\)

Question 31.
If x > y and \(\frac{2 x y}{x^{2}+y^{2}}\) = cosθ, then sinθ = ………………….
A) \(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\)
B) \(\frac{x^{2}+y^{2}}{x^{2}-y^{2}}\)
C) \(\frac{x^{2}-y^{2}}{2 x y}\)
D) \(\frac{2 x y}{x^{2}-y^{2}}\)
Answer:
A) \(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\)

Question 32.
If secθ + tanθ = 3, then cosθ = ………………..
A) \(\frac{3}{4}\)
B) \(\frac{3}{5}\)
C) \(\frac{2}{3}\)
D) \(\frac{2}{5}\)
Answer:
B) \(\frac{3}{5}\)

Question 33.
In ΔABC, if BC = 3, CA = 4, AB = 5, then cos ∠BAC =
A) \(\frac{3}{5}\)
B) \(\frac{3}{4}\)
C) \(\frac{4}{5}\)
D) \(\frac{5}{3}\)
Answer:
B) \(\frac{3}{4}\)

Question 34.
sin⁶ A + cos⁶ A + 3sin²A cos²A =
A) 1
B) -1
C) 0
D) None
Answer:
A) 1

Question 35.
sin²2 30°, sin² 45° and sin² 60° are in
A) AP
B) GP
C) HP
D) AGP
Answer:
A) AP

Question 36.
If sinθ . cosθ = \(\frac {1}{2}\), then θ = …………………
A) 0°
B) 30°
C) 45°
D) 60°
Answer:
C) 45°

Question 37.
If tanθ \(\frac {3}{4}\) , then the value of \(\frac{1-\cos \theta}{1+\cos \theta}\) =
A) 9
B) \(\frac {1}{9}\)
C) 4
D) \(\frac {1}{4}\)
Answer:
B) \(\frac {1}{9}\)

Question 38.
If A, B and C are interior angles of atriangle ABC, then tan (\(\frac{\mathbf{A}+\mathbf{B}}{2}\)) =
A) sin(\(\frac{\mathrm{C}}{2}\))
B) cos(\(\frac{\mathrm{C}}{2}\))
C) tan(\(\frac{\mathrm{C}}{2}\))
D) cot(\(\frac{\mathrm{C}}{2}\))
Answer:
D) cot(\(\frac{\mathrm{C}}{2}\))

Question 39.
If cos A = \(\frac{12}{13}\), then sin A =
A) \(\frac{5}{13}\)
B) \(\frac{5}{12}\)
C) \(\frac{12}{13}\)
D) \(\frac{13}{5}\)
Answer:
A) \(\frac{5}{13}\)

Question 40.
=
A) 0
B) 1
C) -1
D) \(\frac{1}{2}\)
Answer:
B) 1

Question 41.
If tan2A = cot (A – 18°), where 2A is an acute angle, then A =
A) 6°
B) 18°
C) 36°
D) 54°
Answer:
C) 36°

Question 42.
If x = a cosecθ and y = bcotθ, then b²x² – a²y² =
A) a² + b²
B) a²b²
C) \(\frac{a^{2}+b^{2}}{a^{2}-b^{2}}\)
D) None
Answer:
B) a²b²

Question 43.
tan 30°, tan 45°, tan 60° are in
A) AP
B) GP
C) HP
D) None
Answer:
B) GP

Question 44.
cos⁴θ – sin⁴θ =
A) 1 – 2sin²θ
B) 2sin²θ
C) secθ
D) cosecθ
Answer:
A) 1 – 2sin²θ

Question 45.
Sin 0°. Tan 60°. Cos 30°. cosec 45° =
A) 1
B) 0
C) \(\frac{\sqrt{3}}{2}\)
D) ∝
Answer:
B) 0

Question 46.
Ifsin(A + B) = \(\frac{1}{\sqrt{2}}\) and cos (A – B) = \(\frac{1}{\sqrt{2}}\) then ∠B =
A) 60°
B) 45°
C) 30°
D) 0°
Answer:
D) 0°

Question 47.
If sinθ + cosθ = √2 then θ =
A) 0°
C) 45°
B) 30°
D) 60°
Answer:
C) 45°

Question 48.
\(\frac{1-\tan ^{2} 30^{\circ}}{1+\tan ^{2} 30^{\circ}}\) = ………………..
A) \(\frac{1}{2}\)
B) \(\frac{1}{\sqrt{2}}\)
C) \(\frac{\sqrt{3}}{2}\)
D) 1
Answer:
A) \(\frac{1}{2}\)

Question 49.
cos⁴ θ – sin⁴ θ =
A) cos² θ – sin² θ
B) 2cos² θ – 1
C) 1 – 2sin² θ
D) None
Answer:
A) cos² θ – sin² θ

Question 50.
If x = cos θ + sin θ and y = cos θ – sin θ, then x² + y² =
A) 0
B) 1
C) -1
D) 2
Answer:
D) 2

Question 51.
sin (A + B) cos (A – B) + sin (A – B) cos (A + B) =
A) sin 2A
B) sin 2B
C) cos 2A
D) cos 2B
Answer:
A) sin 2A

Question 52.
If sin A = cos B, then A + B =
A) 45°
B) 60°
C) 90°
B) 75°
Answer:
C) 90°

Question 53.
The value of cos 36° cos 54° – sin 36° sin 54° =
A) 1
B) 0
C) 2
D) -1
Answer:
B) 0

Question 54.
The value of \(\frac{1}{1+\cos \theta}+\frac{1}{1-\cos \theta}\) =
A) 2 sec²θ
B) 2secθ
C) 2cosec²θ
D) 2cosecθ
Answer:
C) 2cosec²θ

Question 55.
The value of tan²θ + tan⁴θ
A) sec⁴θ – sec²θ
B) sec²θ – sec⁴θ
C) sin²θ – cos²θ
D) sec²θ – tan²θ
Answer:
A) sec⁴θ – sec²θ

Question 56.
The value of cos 45° . cos 30° . cos 90° . cos 60° =
A) \(\frac{\sqrt{3}}{4 \sqrt{2}}\)
B) \(\frac{\sqrt{3}}{4}\)
C) 0
D) \(\frac{\sqrt{3}}{2 \sqrt{2}}\)
Answer:
C) 0

Question 57.
If x = a cosecθ and y = a cotθ, then which of the following is true ?
A) x² + y² = a²
B) x² – y² = a²
C) x + y = a
D) xy = a
Answer:
D) xy = a

Question 58.
If sin A = \(\frac{7}{25}\),then cot A =
A) \(\frac{25}{7}\)
B) 1
C) \(\frac{24}{25}\)
D) \(\frac{24}{7}\)
Answer:
C) \(\frac{24}{25}\)

Question 59.
cos 12° – sin 78° = ………………
A) 1
B) 1/2
C) 0
D) -1
Answer:
C) 0

Question 60.
If x = cosce θ + cot θ,.y = cosec θ – cot θ, then which of the following is true ?
A) x + y = 0
B) x – y = 0
C) \(\frac{x}{y}\) = 1
D) xy = 1
Answer:
D) xy = 1

Question 61.
Tan²θ – Sec²θ = ………………..
A) 1
B) -1
C) 0
D) ∞
Answer:
B) -1

Question 62.
In Δ ABC, Sin C = \(\frac{3}{5}\). Then Cos A = ……………………..
A) \(\frac{3}{5}\)
B) \(\frac{4}{5}\)
C) \(\frac{5}{4}\)
D) \(\frac{5}{3}\)
Answer:
A) \(\frac{3}{5}\)

Question 63.
If cot A = \(\frac{5}{12}\), then sin A + cos A is ……………….
A) \(\frac{17}{13}\)
B) \(\frac{12}{13}\)
C) \(\frac{5}{13}\)
D) \(\frac{20}{13}\)
Answer:
A) \(\frac{17}{13}\)

Question 64.
Which of following values is not a possible value of sin x ?
A) \(\frac{3}{4}\)
B) \(\frac{3}{5}\)
C) \(\frac{4}{5}\)
D) \(\frac{5}{4}\)
Answer:
D) \(\frac{5}{4}\)

Question 65.
Which of the following is not defined ?
A) Tan0°
B) Tan 90°
C) Cot 90°
D) Sec 0°
Answer:
B) Tan 90°

Question 66.
If Sin A = \(\frac{24}{25}\) then Cot A = ………………………
A) \(\frac{25}{24}\)
B) \(\frac{7}{24}\)
C) \(\frac{24}{7}\)
D) \(\frac{25}{7}\)
Answer:
B) \(\frac{7}{24}\)

Question 67.
In ΔPQR, ∠Q = 90°; PQ = 5 cm; PR = 13 cm then QR =
A) 5 cm
B) 12 cm
C) 13 cm
D) 25 cm
Answer:
B) 12 cm

Question 68.
If Sin A = \(\frac{3}{5}\) then Cos A =
A) \(\frac{3}{4}\)
B) \(\frac{4}{5}\)
C) \(\frac{5}{4}\)
D) \(\frac{4}{3}\)
Answer:
B) \(\frac{4}{5}\)

Question 69.
8 Tan A = 15 then Sin A – Cos A =
A) \(\frac{7}{3}\)
B) \(\frac{7}{17}\)
C) \(\frac{9}{14}\)
D) \(\frac{3}{7}\)
Answer:
B) \(\frac{7}{17}\)

Question 70.
Sin2 60° + Cos2 30° + Tan2 60° =
A) \(\frac{9}{2}\)
B) \(\frac{2}{9}\)
C) \(\frac{1}{9}\)
D) 1
Answer:
A) \(\frac{9}{2}\)

Question 71.
Sin θ = \(\frac{20}{29}\) then Sin² θ + cos² θ =
A) \(\frac{144}{841}\)
B) \(\frac{41}{841}\)
C) 1
D) 0
Answer:
C) 1

Question 72.
If θ = 45° then the value of is
A) 0
B) 1
C) 2
D) ∞
Answer:
B) 1

Question 73.
In ΔABC if Sin A = \(\frac{9}{15}\) then Cosec² A – Cot² A =
A) 1
B) -1
C) 2
D) 3
Answer:
A) 1

Question 74.
(1 + Tan² 45°)² =
A) 1
B) 7
C) 4
D) 9
Answer:
C) 4

Question 75.
Sin²105° + Cos²105° =
A) – 1
B) 1
C) 3
D) 0
Answer:
B) 1

Question 76.
Tan (B + 15°) = \(\frac{1}{\sqrt{3}}\) then B =
A) 60°
B) 80°
C) 70°
D) 15°
Answer:
D) 15°

Question 77
Maximum value of Sin θ =
A) 1
B) \(\frac{1}{2}\)
C) \(\frac{\sqrt{3}}{2}\)
D) \(\frac{1}{\sqrt{2}}\)
Answer:
A) 1

Question 78.
If Sec 2A = Cosec (A – 27°), then the value of ∠A is
A) 35°
B) 37°
C) 39°
D) 21°
Answer:
C) 39°

Question 79.
Sin (A – B) = \(\frac {1}{2}\); Cos (A + B) = \(\frac {1}{2}\) then ∠A is
A) 60°
C) 30°
B) 15°
D) 45°
Answer:
D) 45°

Question 80.
Tan² 60° + 2 Tan² 45° = x Tan 45° Then x =
A) 0
B) 5
C) 1
D) 2
Answer:
B) 5

Question 81.
Sin θ = Cos θ then θ =
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
B) 45°

Question 82.
Sec θ + Tan θ = p then Sin θ =
A) \(\frac{p^{2}-1}{p^{2}+1}\)
B) \(\frac{p}{p^{2}+1}\)
C) \(\frac{p^{2}-1}{p}\)
D) \(\frac{p^{2}+1}{p^{2}-1}\)
Answer:
A) \(\frac{p^{2}-1}{p^{2}+1}\)

Question 83.
2 . Sin 30° . Cos 30° =
A) 1
B) \(\frac{2}{\sqrt{3}}\)
C) \(\frac{\sqrt{3}}{2}\)
D) \(\frac{1}{\sqrt{2}}\)
Answer:
C) \(\frac{\sqrt{3}}{2}\)

Question 84.
Sin 18° = Cos x, then x =
A) 73°
B) 37°
C) 72°
D) 84°
Answer:
C) 72°

Question 85.
Tan θ + Cot θ = 2, then Sin θ =
A) 3
B) 1
C) √2
D) \(\frac{1}{\sqrt{2}}\)
Answer:
D) \(\frac{1}{\sqrt{2}}\)

Question 86.
The value of Cos 0° + Sin 90° + √2 Sin 45° =
A) 5
C) 1
B) 4
D) 3
Answer:
D) 3

Question 87.
Sin θ = \(\frac {1}{2}\) then cot θ =
A) 3
B) 7
C) √3
D) 2√3
Answer:
C) √3

Question 88.
In ΔABC, a = 3 units; b = 4 units; c = 5 units. Then cos A =
A) \(\frac{3}{5}\)
B) \(\frac{3}{4}\)
C) \(\frac{5}{3}\)
D) \(\frac{4}{5}\)
Answer:
D) \(\frac{4}{5}\)

Question 89.
Cos (A – B) = \(\frac{1}{2}\); Sin B = \(\frac{1}{\sqrt{2}}\) , then the value of A.
A) 15°
B) 105°
C) 90°
D) 60°
Answer:
B) 105°

Question 90.
Sin 60° Cos 30° + Cos 60° Sin 30° Value is ……………………
A) \(\frac{1}{2}\)
B) 1
C) \(\frac{\sqrt{3}}{2}\)
D) \(\frac{2}{\sqrt{3}}\)
Answer:
B) 1

Question 91.
√3 Tan θ = 1, then θ =
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
A) 30°

Question 92.
In a ΔABC if ∠B = 90° and Tan C = \(\frac {5}{12}\) , then the length of the hypotenuse is
A) 6
B) 13
C) 21
D) 17
Answer:
B) 13

Question 93.
Tan² 60° + 4 Cos² 45° + 3 Sec² 30° + 5 Cos² 90° =
A) 7
B) 8
C) 9
B) 10
Answer:
A) 7

Question 94.
Sec² 27° – Cot² 63° =
A) 3
B) 0
C) 1
D) 2
Answer:
B) 0

Question 95.
=
A) Sin θ
B) Cos θ
C) Sec θ
D) Cosec θ
Answer:
D) Cosec θ

Question 96.
Sin² θ (1 + Cot²θ) =
A) Cos² θ
B) Sec² θ
C) Tan² θ
D) 1
Answer:
D) 1

Question 97.
If A = 45°, then (1 + Tan A) (1 + Tan²A) (1 + Tan³ A) =
A) 6
B) 8
C) 4
D) 2
Answer:
B) 8

Question 98.
Sin² θ . Cot² θ + Cos² θ . Tan² θ =
A) 0
B) 2
C) 1
D) -1
Answer:
C) 1

Question 99.
Tan 45° + 2 Tan² 60° =
A) 6
B) 7
C) 8
D) 9
Answer:
B) 7

Question 100.
Sin 2A = 2 Sin A, then ∠A =
A) 0°
B) 30°
C) 45°
D) 60°
Answer:
A) 0°

Question 101.
If x Sin (90° – θ) Cot (90° – θ) = Cos (90° – θ) then x =
A) 0
B) 1
C) – 1
D) 2
Answer:
B) 1

Question 102.
If Tan θ + Cot θ = 5, then the value of Tan² θ + Cot² θ =
A) 25
B) 23
C) 27
D) 15
Answer:
B) 23

Question 103.
If Cosec θ – Cot θ = \(\frac {1}{4}\) then the value of Cosec θ + Cot θ is
A) 1
B) -1
C) \(\frac {1}{4}\)
D) 4
Answer:
D) 4

Question 104.
Sin 40°=
A) Sin × 40°
B) Sin + 40°
C) Sin 20° + Sin 20°
D) A real number
Answer:
D) A real number

Question 105.
If ΔXYZ is a right angled isosceles triangle and ∠Y = 90° then XZ =
A) √2 XY
B) √3 XY
C) 2 XY
D) XY²
Answer:
A) √2 XY

Question 106.
Tan θ is not defined, then θ =
A) 50°
B) 60°
C) 180°
D) 90°
Answer:
D) 90°

Question 107.
Sin (90° – θ) =
A) Sin θ
B) Cos θ
C) Cosec θ
D) Sec θ
Answer:
B) Cos θ

Question 108.
Tan 81° =
A) Cos 9°
B) Sin 9°
C) Cot 9°
D) Tan 9°
Answer:
C) Cot 9°

Question 109.
Sin A. Cos (90° – A) + Cos A. Sin (90° – A) =
A) Sin²A
B) Cos²A
C) 0
D) 1
Answer:
D) 1

Question 110.
=
A) Tan² θ
B) Cot² θ
C) Sin² θ
D) Cos² θ
Answer:
A) Tan² θ

Question 111.
a) Sin (A + B) = Sin A Cos B + Cos A Sin B
b) Sin (A – B) = Sin A Cos B – Cos A Sin B
Which is correct in the above statements?
A) a is correct
B) b is correct
C) Both a and b are correct
D) Both a and b are wrong
Answer:
C) Both a and b are correct

Question 112.
a) Sin 30° = 1
b) Cos 30° = \(\frac {1}{2}\)
Which is correct in the above statements?
A) a is correct
B) Both a and b are correct
C) b is correct
D) Both a and b are wrong
Answer:
D) Both a and b are wrong

Question 113.
a) Sin² θ + Cos² θ = 1
b) Tan² θ + Sec² θ = 1
Which is correct in the above statements?
A) b is correct
B) a is correct
C) Both a and b are correct
D) Both a and b are wrong
Answer:
B) a is correct

Question 114.
Sin (A – B) = \(\frac {1}{2}\); Cos (A + B) = \(\frac {1}{2}\) is true for ……………….
A) 0° > A + B > 90°
B) A > B
C) 0°< A + B < 90°and A > B
D) A < B and A > B
Answer:
C) 0°< A + B < 90°and A > B

Question 115.
Sin 81° + Tan 81° can be expressed as …………………..
A) Sin 9° + Tan 9°
B) cos 9° + cot 9°
C) Sin 9° + Cot 9°
D) Cos 9° + Tan 9°
Answer:
B) cos 9° + cot 9°

Question 116.
Sin (A + B) = Sin A + Sin B is not true for
A) A = 30°; B = 60°
B) A = 30°; B = 45°
C) A = 45°; B = 60°
D) A = 60°; B = 30°
Answer:
D) A = 60°; B = 30°

Question 117.
i) Sec θ = \(\frac{\text { Length of the hypotenuse }}{\text { Length of the side adjacent to } \theta}\)
ii) Cot θ = \(\frac{\text { Length of the side opposite to } \theta}{\text { Length of the side adjacent to } \theta}\)
A) (i), (ii) are true
B) (i), (ii) are false
C) (i) is false (ii) is true
D) (i) is true (ii) is false
Answer:
D) (i) is true (ii) is false

Question 118.
Ramu said Cos A = 2 ; Ravi said Cos A = 1. Do you agree with whom ?
A) Ramu
B) Ravi
C) Ramu and Ravi
D) Nobody
Answer:
B) Ravi

Question 119.
In ΔABC, ∠B = 90° then Sin A =
A) \(\frac{\mathrm{AC}}{\mathrm{AB}}\)
B) \(\frac{\mathrm{AB}}{\mathrm{AC}}\)
C) \(\frac{\mathrm{BC}}{\mathrm{AC}}\)
D) \(\frac{\mathrm{BC}}{\mathrm{AB}}\)
Answer:
C) \(\frac{\mathrm{BC}}{\mathrm{AC}}\)

Question 120.
In a right angled triangle the adjacent side of 30°
A) Opposite side of 30°
B) Hypotenuse
C) Opposite side of 60°
D) Adjacent side of 60°
Answer:
C) Opposite side of 60°

Question 121.
Cos θ. Tan θ =
A) Sinθ
B) Cosθ
C) Cot θ
D) Sin² θ . Cos θ
Answer:
A) Sinθ

Question 122.
If Cos θ = \(\frac{a}{b}\) then Cosec θ is equal to
A) \(\frac{\mathrm{b}}{\mathrm{a}}\)
B) \(\frac{b}{\sqrt{b^{2}-a^{2}}}\)
C) \(\frac{\sqrt{b^{2}-a^{2}}}{b}\)
D) \(\frac{a}{\sqrt{b^{2}-a^{2}}}\)
Answer:
B) \(\frac{b}{\sqrt{b^{2}-a^{2}}}\)

Question 123.
Sec θ = \(\frac{\mathbf{m}+\mathbf{n}}{2 \sqrt{\mathbf{m n}}}\) then Cosec θ =
A) \(\frac{\mathrm{mn}}{2}\)
B) \(\frac{\mathrm{m}+\mathrm{n}}{2}\)
C) \(\frac{m-n}{m+n}\)
D) \(\frac{\mathrm{mn}}{\mathrm{m}+\mathrm{n}}\)
Answer:
C) \(\frac{m-n}{m+n}\)

Question 124.
Cos² θ (1 + Tan²θ) =
A) – Sin² θ
B) 1
C) Sin θ
D) – 1
Answer:
B) 1

Question 125.


Answer:

Question 126.
Express Tan θ in terms of Sec θ.

Answer:

Question 127.
– cotθ =
A) Cot θ
C) Sec θ
B) Cosec θ
D) Tan θ
Answer:
D) Tan θ

Question 128.
=
A) Cot θ
C) Sec θ
B) Tan θ
D) Cosec θ
Answer:
A) Cot θ

Question 129.
If cos θ = \(\frac{2 \sqrt{m n}}{m+n}\) ,then sin θ =
A) \(\frac{m+n}{m-n}\)
B) \(\frac{m-n}{m+n}\)
C) \(\frac{2 \sqrt{\mathrm{mn}}}{\mathrm{m}+\mathrm{n}}\)
D) \(\frac{\mathrm{m}+\mathrm{n}}{\mathrm{mn}}\)
Answer:
B) \(\frac{m-n}{m+n}\)

Question 130.
=
A) 2 Sec θ
B) 2 Sec² θ
C) 2 Cosec θ
D) 2 Cosec² θ
Answer:
B) 2 Sec² θ

Question 131.
Sec θ (1 – Sin θ) (Sec θ + Tan θ) =
A) 0
B) 1
C) 2
D) -1
Answer:
B) 1

Question 132.
The ratio of lengths of opposite sides of 30°, 60°, 90° is
A) 1 : 2 : 3
B) 1 : 1 : √2
C) 1 : 3 : 2
D) 1 : √3 : 2
Answer:
D) 1 : √3 : 2

Question 133.
If Sin A = Cos B, then ……………………. (A, B are acute)
A) A = B
B) A + B = 180°
C) A = 90° + B
D) A + B = 90°
Answer:
D) A + B = 90°

Question 134.
=
A) – Tan² A
B) -Tan⁴ A
C) 1
D) – Sec² A
Answer:
B) -Tan⁴ A

Question 135.
If Tan θ + Sec θ = 8, then Sec θ – Tan θ value is
A) 8
B) \(\frac {1}{8}\)
C) 6
D) 64
Answer:
B) \(\frac {1}{8}\)

Question 136.
=
A) Sin A
B) 1 – Sin²A
C) Cos A
D) 1
Answer:
C) Cos A

Question 137.
Sin θ = \(\frac{\mathrm{a}}{\mathrm{b}}\); Cos θ = \(\frac{\mathbf{c}}{\mathbf{d}}\) then Cot θ =
A) \(\frac{a b}{c d}\)
B) \(\frac{\mathrm{bc}}{\mathrm{ad}}\)
C) \(\frac{c a}{b d}\)
D) \(\frac{\mathrm{ad}}{\mathrm{bc}}\)
Answer:
B) \(\frac{\mathrm{bc}}{\mathrm{ad}}\)

Question 138.
Sin θ . Cot θ . Sec θ =
A) 2
B) -1
C) 1
D) 0
Answer:
C) 1

Question 139.
=
A) Sin θ
B) Cos θ
C) Tan θ
D) Cot θ
Answer:

Question 140.
Sin³ θ Cos θ + Cos³ θ Sin θ =
A) Sin θ + Cos θ
B) Sin θ Cos θ
C) Sin θ
D) Cot θ
Answer:
B) Sin θ Cos θ

Question 141.
Tan θ + Cot θ = 2, then Tan² θ + Cot² θ =
A) 4
B) 2
C) 6
D) 1
Answer:
B) 2

Question 142.
=
A) Sec θ + Tan θ
B) Sec θ – Tan θ
C) Sec² θ + Tan² θ
D) Sec² θ – Tan² θ
Answer:
A) Sec θ + Tan θ

Question 143.
. Cot α =
A) Tan α
C) 1
B) Cota
D) -1
Answer:
C) 1

Question 144.
If A, B and C are interior angles of a triangle ABC, then Sin (\(\frac{B+C}{2}\)) =
A) Sin \(\frac{\mathrm{A}}{2}\)
B) Cos \(\frac{\mathrm{A}}{2}\)
C) – Sin \(\frac{\mathrm{A}}{2}\)
D) – Cos \(\frac{\mathrm{A}}{2}\)
Answer:
B) Cos \(\frac{\mathrm{A}}{2}\)

Question 145.
can be expressed as …………….
A) Sin 0°
B) cos 90°
C) Sin 0° Cos 90°
D) Sin 60°
Answer:
D) Sin 60°

Question 146.
Cosec² A – Cot² A = 1 is true for all
A) 0° > A ≥ 90°
B) 0° < A ≥ 90° C) 0° > A < 90°
D) 0° < A ≤ 90°
Answer:
D) 0° < A ≤ 90°

Question 147.
From the adjacent figure ON = x; PN = y; OP = r ; ∠PON = θ and ∠PNO = 90° then
i) cos θ =

A) \(\frac{\mathrm{y}}{\mathrm{r}}\)
B) \(\frac{\mathrm{y}}{\mathrm{x}}\)
C) \(\frac{\mathrm{x}}{\mathrm{r}}\)
D) \(\frac{\mathrm{r}}{\mathrm{x}}\)
Answer:
C) \(\frac{\mathrm{x}}{\mathrm{r}}\)

ii) Tan θ =
A) \(\frac{x}{y}\)
B) \(\frac{\mathrm{y}}{\mathrm{x}}\)
C) \(\frac{\mathrm{r}}{\mathrm{x}}\)
D) \(\frac{\mathbf{r}}{\mathrm{y}}\)
Answer:
B) \(\frac{\mathrm{y}}{\mathrm{x}}\)

Question 148.
From the adjacent figure ΔABC, ∠B = 90°; ∠C = θ, then Sec θ =

A) \(\frac{17}{15}\)
B) \(\frac{17}{8}\)
C) \(\frac{15}{17}\)
D) \(\frac{15}{8}\)
Answer:
A) \(\frac{17}{15}\)

Question 149.
Which of the following represents Sin θ = \(\frac{21}{29}\) ?

Answer:

Question 150.
From the adjacent figure Sin C = \(\frac{3}{5}\) then Cos A =

A) \(\frac{5}{4}\)
B) \(\frac{5}{3}\)
C) \(\frac{3}{5}\)
D) \(\frac{4}{5}\)
Answer:
C) \(\frac{3}{5}\)

Question 151.
From this figure length of AB is
A) 20 √3 nits
B) \(\frac{20}{\sqrt{3}}\) mts
C) 60 mts
D) 30 mts
Answer:
A) 20 √3 nits

Question 152.
From this figure ∠QPR =
A) 30°
B) 60°
C) 45°
D) 90°
Answer:
B) 60°

Question 153.
From the adjacent figure the length of the chord is

A) 3 cm
B) 4 cm
C) 6 cm
D) 12 cm
Answer:
C) 6 cm

Question 154.
From the adjacent figure length of Hypotenuse is

A) 5
B) 12
C) 13
D) 25
Answer:
C) 13

Question 155.
For finding ‘θ’ from the adjacent figure the trigonometric ratio used is

A) Sine
B) Cosine
C) Tangent
D) Cosecant
Answer:
C) Tangent