Practice the AP 10th Class Maths Bits with Answers Chapter 11 Trigonometry on a regular basis so that you can attempt exams with utmost confidence.

## 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) $$\frac{6}{5}$$
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) $$\frac{\sqrt{3}}{2}$$
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°
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
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) $$\frac{2}{7}$$
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) $$\frac{1}{\sqrt{2}}$$
C) 1

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

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

Question 9.
tan 36°. tan 54° + sin 30° = ………………..
A) $$\frac{3}{2}$$
B) $$\frac{1}{2}$$
C) 2
D) $$\frac{2}{3}$$
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) $$\frac{7}{24}$$
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)
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) $$\frac{\mathrm{AC}}{\mathrm{AB}}$$
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) $$\frac{\sqrt{1-\sin ^{2} \theta}}{\sin \theta}$$
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
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) $$\frac{1}{3}$$
B) $$\frac{1}{9}$$

Question 16.
tan θ is not defined when ‘θ’ is
A) 0°
B) 30°
C) 60°
D) 90°
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
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°
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) $$\frac{\sqrt{3}}{2}$$
A) $$\frac{5}{4}$$

Question 20.
If Sin A = Cos B then A + B = ……………………..
A) 60°
B) 90°
C) 45°
D) 120°
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) $$\frac{3}{7}$$)
B) $$\frac{1}{6}$$

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

Question 23.
tan 2A = 1 then A = …………………..
A) 45.5
B) 60.5
C) 22.5
D) 30.5
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 + $$\frac{z^{2}}{c^{2}}$$
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
C) 1

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

Question 27.
If cotθ + cosecθ = 5, then cosθ = ………………..
A) $$\frac{12}{13}$$
B) $$\frac{26}{24}$$
C) $$\frac{5}{13}$$
D) $$\frac{13}{12}$$
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
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) $$\frac{7}{8}$$
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) $$\frac{2 \mathrm{P}}{1-\mathrm{P}^{2}}$$
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) $$\frac{2 x y}{x^{2}-y^{2}}$$
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) $$\frac{2}{5}$$
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) $$\frac{5}{3}$$
B) $$\frac{3}{4}$$

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

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

Question 36.
If sinθ . cosθ = $$\frac {1}{2}$$, then θ = …………………
A) 0°
B) 30°
C) 45°
D) 60°
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) $$\frac {1}{4}$$
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($$\frac{\mathrm{C}}{2}$$)
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) $$\frac{13}{5}$$
A) $$\frac{5}{13}$$

Question 40.
=
A) 0
B) 1
C) -1
D) $$\frac{1}{2}$$
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°
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
B) a2b2

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

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

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

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

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

Question 53.
The value of cos 36° cos 54° – sin 36° sin 54° =
A) 1
B) 0
C) 2
D) -1
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
C) 2cosec2θ

Question 55.
The value of tan2θ + tan4θ
A) sec4θ – sec2θ
B) sec2θ – sec4θ
C) sin2θ – cos2θ
D) sec2θ – tan2θ
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) $$\frac{\sqrt{3}}{2 \sqrt{2}}$$
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
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) $$\frac{24}{7}$$
C) $$\frac{24}{25}$$

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

Question 61.
Tan2θ – Sec2θ = ………………..
A) 1
B) -1
C) 0
D) ∞
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) $$\frac{5}{3}$$
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) $$\frac{20}{13}$$
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) $$\frac{5}{4}$$
D) $$\frac{5}{4}$$

Question 65.
Which of the following is not defined ?
A) Tan0°
B) Tan 90°
C) Cot 90°
D) Sec 0°
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) $$\frac{25}{7}$$
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
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) $$\frac{4}{3}$$
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) $$\frac{3}{7}$$
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
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
C) 1

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

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

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

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

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

Question 78.
If Sec 2A = Cosec (A – 27°), then the value of ∠A is
A) 35°
B) 37°
C) 39°
D) 21°
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°
D) 45°

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

Question 81.
Sin θ = Cos θ then θ =
A) 30°
B) 45°
C) 60°
D) 90°
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) $$\frac{p^{2}+1}{p^{2}-1}$$
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) $$\frac{1}{\sqrt{2}}$$
C) $$\frac{\sqrt{3}}{2}$$

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

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

Question 87.
Sin θ = $$\frac {1}{2}$$ then cot θ =
A) 3
B) 7
C) √3
D) 2√3
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) $$\frac{4}{5}$$
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°
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) $$\frac{2}{\sqrt{3}}$$
B) 1

Question 91.
√3 Tan θ = 1, then θ =
A) 30°
B) 45°
C) 60°
D) 90°
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
B) 13

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

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

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

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

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

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

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

Question 100.
Sin 2A = 2 Sin A, then ∠A =
A) 0°
B) 30°
C) 45°
D) 60°
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
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
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
D) 4

Question 104.
Sin 40°=
A) Sin × 40°
B) Sin + 40°
C) Sin 20° + Sin 20°
D) A real number
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
A) √2 XY

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

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

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

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

Question 110.
=
A) Tan2 θ
B) Cot2 θ
C) Sin2 θ
D) Cos2 θ
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
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
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
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
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°
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°
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
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
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) $$\frac{\mathrm{BC}}{\mathrm{AB}}$$
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°
C) Opposite side of 60°

Question 121.
Cos θ. Tan θ =
A) Sinθ
B) Cosθ
C) Cot θ
D) Sin2 θ . Cos θ
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) $$\frac{a}{\sqrt{b^{2}-a^{2}}}$$
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) $$\frac{\mathrm{mn}}{\mathrm{m}+\mathrm{n}}$$
C) $$\frac{m-n}{m+n}$$

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

Question 125.

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

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

Question 128.
=
A) Cot θ
C) Sec θ
B) Tan θ
D) Cosec θ
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) $$\frac{\mathrm{m}+\mathrm{n}}{\mathrm{mn}}$$
B) $$\frac{m-n}{m+n}$$

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

Question 131.
Sec θ (1 – Sin θ) (Sec θ + Tan θ) =
A) 0
B) 1
C) 2
D) -1
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
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°
D) A + B = 90°

Question 134.
=
A) – Tan2 A
B) -Tan4 A
C) 1
D) – Sec2 A
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
B) $$\frac {1}{8}$$

Question 136.
=
A) Sin A
B) 1 – Sin2A
C) Cos A
D) 1
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) $$\frac{\mathrm{ad}}{\mathrm{bc}}$$
B) $$\frac{\mathrm{bc}}{\mathrm{ad}}$$

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

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

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
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
B) 2

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

Question 143.
. Cot α =
A) Tan α
C) 1
B) Cota
D) -1
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 $$\frac{\mathrm{A}}{2}$$
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°
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°
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) $$\frac{\mathrm{r}}{\mathrm{x}}$$
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) $$\frac{\mathbf{r}}{\mathrm{y}}$$
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) $$\frac{15}{8}$$
A) $$\frac{17}{15}$$

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

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) $$\frac{4}{5}$$
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
A) 20 √3 nits

Question 152.
From this figure ∠QPR =
A) 30°
B) 60°
C) 45°
D) 90°
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
C) 6 cm

Question 154.
From the adjacent figure length of Hypotenuse is

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