CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 02

Question. What is the value of sin² 5° + sin² 10° + sin² 80° + sin² 85° ?
(a) 0
(b) 1
(c) 2
(d) 3

Answer: C

Question. If tan 26° tan19°/ x(1 tan 26° tan19° ) = cos60^o, what is the value of x ?
(a) 1
(b) 2
(c) 2
(d) 3

Answer: C

Question. If 4tanΘ = 1, find the value of 4sinΘ – 2cosΘ / 4sinΘ + 3cosΘ
(a) 1/2
(b) 1/6
(c) 2/3
(d) 1/3

Answer: B

Question. If sin A + sin2 A = 1 , find the value of the expression (cos2 A + cos4 A) .
(a) 1
(b) 1/2
(c) 2
(d) 3

Answer: A

Question. Find the value of sin 15° .
(a) √3+1/√2
(b) √3 -1/√2
(c) √3+1/2√2
(d) √3 -1/2√2

Answer: D

Question. What is the value of sinθ + cos30° – tan45°+ cosec 60° + cot90° ?
(a) 7√3 – 6/6
(b) 6 + 7√3/6
(c) 0
(d) 2

Answer: A

Question. If sin θ = 1/2 , what are the respective possible values of 9 between 0 and 2π ?
(a) 210° and 300°
(b) 240° and 330°
(c) 240° and 300°
(d) 210° and 330°

Answer: D

Question. In terms of radians. what is the equivalent of 45° ?
(a) 25π
(b) 0.25π
(c) 180°π /45°
(d) 45°/π

Answer: D

Question. ΔABC is right angled at A. If AC = 8 cm and AB = 6 cm, what is the value of cosec B?
(a) 5/4
(b) 3/4
(c) 4/3
(d) 4/5

Answer: A

Question. ΔABC is right angled at A .lf BC = √2 and AB = AC =1, what is the measure of ∠B ?
(a) 60°
(b) 45°
(c) 30°
(d) 90°

Answer: B

Question. If the shadow of a boy ‘x’ metres high is 1.6m and the angle of elevation of the sun is then the value of ‘x’ is 45°
(a) 0.8 m
(b) 1.6 m
(c) 3.2 m
(d) 2 m

Answer: B

Question. If the angle of depression of an object from a 75m high tower is 30° , then the distance of the object from the tower is
(a) 25√3 m
(b) 50√3 m
(c) 100√3 m
(d) 75√3 m

Answer: D

Question. In a right triangle ABC, If AC = BC and then find its value
(a) 50√3
(b) 150 m
(c) None of these
(d) 100√3 m

Answer: D

Question. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50m high, then the height of the hill is
(a) 50√3 m
(b) 150m
(c) 150√3 m
(d) 100√3 m

Answer: B

Question. The angles of elevation of the top of a tower from two points on the ground at distances 8 m and 18 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
(a) 12 m
(b) 18 m
(c) 8 m
(d) 16 m

Answer: A

Question. Find the value of 2/3 (cos⁴ 30^o – sin4 45^o) – 3 (sin² 60^o – sec² 45^o) + 1/4 cot² 30^o
(a) 15/4
(b) 3/4
(c) 2(65/4)
(d) 4(17/24)

Answer: D

Fill in the blanks.

Question. sin A _____________ when A increases from 0° to 90°.
Answer: increases

Question. cos A _____________ when A increases from 0° to 90°.
Answer: decreases

Question. cot 90° is ___________.
Answer: 0°

Question. cos0° × cos10° × cos30° × cos80° × cos90° = _____________ .
Answer: 0

One words

Question. Can the value of secant of an angle be greater than 1?
Answer: Yes

Question. If 2sin²θ -cos² θ = 2, then find the value of θ.
Answer: θ = 90°

Question. What will be the change in the value of cosq if we decrease the value of θ?
Answer: It will increase

Question. What is the reciprocal of sec A?
Answer: cos A

Question. Is tan A the reciprocal of cot A?
Answer: Yes

Question. Define an identity.
Answer: An equation which holds true for all values of the variable.

Write True or False.

Question. The value of the expression (sin70° -cos70°) is negative.
Answer: False

Question. If cosA+cos²A =1, then sin²A+sin⁴ A=1.    
Answer: True

Question. If tan A = 3/4 , then cos A = 4/5
Answer: True

Question. In ΔABC, if ∠A +∠C = 90°, then sin A = cosC
Answer: True

Question. cot 60° = tan (90° – 30°)
Answer: False

Question. The value of 2sinθ can be a+1/a, where a is a positive number and a ≠ 1.
Answer: False