# MCQ Questions for Class 10 Trigonometry

Please refer to the MCQ Questions for Class 10 Maths Trigonometry with Answers. The following Trigonometry Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Trigonometry Class 10 MCQ Questions with Answers

Please see below Trigonometry Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. If tan A= 3/4 , then the value of sec A is 1v
(a) 5/3
(b) 5/4
(c) 4/3
(d) 4/5

B

Question. Given that 3cotθ = 4, then (5sinθ-3cosθ)/(5sinθ+3cosθ) is equal to
(a) 1/9
(b) 9
(c) 2/5
(d) 1/2

A

Question. If sinA +sin2 A=1, then the value of the expression cos2A+cos4A is
(a) 1
(b) 1/2
(c) 2
(d) 3

A

Question. The value of the expression cossec (58°+1 ) – sec (32°+1 )/tan45 tan(45+θ )-cot(45-θ) is
(a) 1
(b) 1/2
(c) 0
(d) 2

C

Question. Given that tana = √3 and tanb = 1/√3 , then the value of (a +b) is
(a) 0°
(b) 30°
(c) 60°
(d) 90°

D

Question. The value of (tan2 60°+sin2 30°)/(tan2 45°+cos230°)
(a) 7/11
(b) 11/13
(c) 13/11
(d) 11/7

D

Question. Which of the following is not a trigonometric identity?
(a) sec 2θ -tan2θ =1
(b) cosec 2θ -sin2θ =1
(c) cot 2θ -cosec 2θ = -1
(d) 1-cos2θ = sin2θ

B

Question. If cosθ = 1/2 , sinΦ =1/2 , then value of θ +Φ
(a) 30°
(b) 60°
(c) 90°
(d) 120°

C

Question. The value of the expression 1/2 tan60° -sin60° +2cos60° is
(a) 1/2
(b) 2
(c) 1
(d) 0

C

Question. If cos(α + β ) = 0 , what is the value of sin(α – β) ?
(a) cosβ
(b) cos2β
(c) sinα
(d) sin 2α

B

Question. If tanθ + secθ = 2 , 0 ≤ θ ≤ π/2 find the value of the tanθ .
(a) 3/4
(b) 5/4
(c) 3/2
(d) 5/2

A

Question. If tan x = x/y , where x and y are whole numbers, find sin x .
(a) y/√y2 – x2
(b) x/√x2 + y2
(c) y/√x2 + y2
(d) x/√y2 – x2

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

A

Question. If cos9α = sinα a and 9α < 90o , what is the value of tan 5 a?
(a) 1/√3
(b) √3
(c) 1
(d) 1/2

C

Question. If sinθ – cosθ = 0 , find the value of (sin4θ + cos4 θ) .
(a) 1
(b) 3/4
(c) 1/2
(d) 1/4

C

Question. Find the value of sin(45 +θ ) – cos(45 – θ) .
(a) 2cosθ
(b) 0
(c) 2sinθ
(d) 1

B

Question. What is the value of tan 7° tan 23° tan 60° tan 67° tan 83° ?
(a) 1/√3
(b) √3
(c) 1
(d) ∝

B

Question. If secθ + b tanθ = p , what is the value of cosθ ?
(a) p2 + 1/p2 – 1
(b) p2 – 1/(p2 + 1)2
(c) 2p/p2 + 1
(d) 4p1/(p2 + 1)2

C

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

C

Question. If sin B = 1/2 , find the value of 3 3cosB – 4cos3 B.
(a) 1/2
(b) 1
(c) 2
(d) 0

D

Question. If 4 tanθ = 1, find the value of 4sin θ – 2 cosθ/4 sinθ + 3cos θ .
(a) 1/2
(b) 1/6
(c) 2/3
(d) 1/3

B

Question. If √3 tanθ = 3sin θ , find the value of sin2 θ – cos2θ .

(a) √2/√3
(b) 1/3
(c) 1/2
(d) 1/√3

B

Question. If ΔABC is right angled at C, find the value of cos(A + B) .
(a) 0
(b) 1
(c) 1/2
(d) √3/2

A

Question. If cosecθ = 13/12 , find the value of 2sin θ – 3cos θ/4sin θ – 9 cosθ .

(a) 0
(b) 1
(c) 3
(d) 2

C

Question. If 8 tan A =15, find the value of sin A – cosA/sinA + cosA .
(a) 7/23
(b) 11/23
(c) 13/23
(d) 17/23

A

Question. If sin(A + B) =1 and cos(A-B) = √3/2 , find A and B.
(a) 45°,45°
(b) 90°,45°
(c) 45°, 30°
(d) 60°, 30°

D

Question. The value of (tan 1° tan 2° tan 3° . . . tan 89°) is
(a) 0
(b) 1
(c) 2
(d) 1/2

B

Question. If 5tanθ =12, then (5sinθ-cosθ)/(5sinθ+cosθ) is equal to
(a) 12/13
(b) 5/13
(c) 11/13
(d) 13/11

C

Question. If DABC is right-angled at C, then cot (A + B) is
(a) 0
(b) 1
(c) 1/√2
(d) not defined

A

Question. √(1 +tan2θ) is equal to:
(a) cot θ
(b) cosθ
(c) cosec θ
(d) sec θ

D

Question. If sinθ -cosθ = 0, then the value of (sin4θ +cos4θ ) is
(a) 1/4
(b) 1/2
(c) 34
(d) 1

B

Question . The reciprocal of sin A is cos A, A ≠ 0.

F

Question. cot A is not defined for A = 0°

T

Question. Trigonometry deals with measurement of components of triangles.

T

Question. cot A is the reciprocal of tan A, A ≠ 90°.

T

Question. cos A is the abbreviation used for the cosecant of angle A.

F

Question. sin2 A = (sin A)2

T

Question. Sum of the squares of sin A and cos A is 1.

T

Question. The value of cos90° is 1.

F

Question. The values of sin A and cos A can never exceed 1.

T

Question. sec A and cosec A can take any value on the real number line.

F

Question. sin(90° – A) = cos A

T

Question. cos(90°-A)= sec A

F

Question. The value of sinq +cosq is always greater than 1

F

Question. (1 -cos2θ)sec2θ = tanθ

T

Question. tanq increases faster than sinq as q increases.

T

Question. sinq = 5/3 for some angle θ.

F

Question. tan70°tan20° =1

T

Question. The value of the expression (cos2 20° -sin2 67°) is positive.

T

Question. The trigonometric ratios can be applied in any triangle.

F

Question. The values of sin A and sin B will always be same for a right DABC right-angled at C.

F

Question. How is cotΘ expressed in terms of sinΘ ?

B

Question. Find the value of the expression sin2 22o + sin2 68o / coso22o + cos2 680 + sin63 + cos63 sin 27o
(a) 3
(b) 2
(c) 1
(d) 0

B

Question. Find sin3ø + cos3ø / sinø + cosø
(a) 1 + sinø cosø
(b) 1- sincø cosø
(c) 1 – sinø tanø
(d) 1

A

Question. Find the value of 1 + tan 75o / 1 – tan 75o
(a) 2/√3
(b) √3
(c) -√3
(d) 1/√3

C

Question. If x = a secΘ + b tanΘ and y = b secΘ + a tanΘ , find x2 – y2 .
(a) 4absecΘ + α tanΘ
(b) α2 – b2
(c) b2 – α2
(d) α2 + b2

B

Question. If sinΘ – cosΘ = 0 , find the value of (sin4Θ + cos4Θ)
(a) 1
(b) 3/4
(c) 1/2
(d) 1/4

C

Question. If cos3x = cos 30o sin 60o – sin 30o cos 60o, find the value of x.
(a) 60o
(b) 45o
(c) 20o
(d) 30o

C

Question. If sin(A+B) =1 and 3 cos(A-B) = √3/2, find A and B.
(a) 45o,45o
(b) 90o,45o
(c) 45o, 30o
(d) 60o, 30o

D

Question. If cosecΘ 13/12 , find the value of 2sinΘ – 3cosΘ / 4sinΘ – 9cosΘ

(a) 0
(b) 1
(c) 3
(d) 2

C

Question. If sin B = 1/2, find the value of 3 3cosB – 4cos2 B.
(a) 1/2
(b) 1
(c) 2
(d) 0

D

Question. Find the value of √1 – cos A/1 + cos A
(a) sec A – cot A
(b) cosec A – cot A
(c) 0
(d) 1

C

Question. If tan x = sin 45o cos45o + sin30o , find the value of x .
(a) 30o
(b) 60o
(c) 45o
(d) 90o

C

Question. What is the value of sin0o + cos30o – tan45o + cosec 60o + cot90o ?
(a) 7√3 – 6 / 6
(b) 6 + 7√3 / 6
(c) 0
(d) 2

A

Question. Find the value of the expression [cossec (75o + Θ ) – sec(15o – Θ) – tan(55o + Θ) + cot (35o)]
(a) – 1
(b) 0
(c) 1
(d) 3/2

B

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

D

Question. If cos(αβ ) = 0 , what is the value of sin(α – β) ?
(a) cos β
(b) cos 2 β
(c) sin α
(d) sin 2 α

B

Question. Given sin2 Θ + 1/sin2 Θ, what is the value of sinΘ + cosΘ ?
(a) 25/31
(b) 31/25
(c) 24/25
(d) 31/24

B

Question. If tanΘ + secΘ = 2 , 0 < Θ < π/2 find the value of the tanΘ .
(a) 3/4
(b) 5/4
(c) 3/2
(d) 5/2

A

Question. What is the value of Θ if √3 tan 2Θ – 3 = 0 ?
(a) 45o
(b) 90o
(c) 30o
(d) 60o

C

Question. If sin 2 (2/1, 3/2, 4/3……x – 1/x – 2) = 1, 0 < x < 100, find the value of x .
(a) 91o
(b) 80o
(c) 49o
(d) 46o

D

Question. If secΘ = 2p and tanΘ =2/p find the value

(a) 1/2
(b) 1/√2
(c) 1/4
(d) 1/8

A

Question. Graphs of y = sin x and y = cos x , where 0 < x < π/2 intersect at a point. Find abscissa.
(a) π/6
(b) π/4
(c) π/3
(d) 0

B

Question. What is the value of tan 70 tan 230 tan 600 tan 670 tan 830 ?
(a) 1/√3
(b) ) √3
(c) 1
(d) ∝

B

Question. ΔABC is right angled at A .lf BC √2 and AB = AC =1, what is the measure of ∠B ?
(a) 600
(b) 450
(c) 300
(d) 900

B

Question. ΔABCis an isosceles triangle with the unequal side measuring 12 cm. If both the equal sides measure 19 cm, what is the measure of ∠BAC?
(a) 36.8o
(b) 68o
(c) 38o
(d) 60o

A

Question. The value of (sin2θ + 1/1 +tan2 θ) equals
(a) 1
(b) 8
(c) 11
(d) 24

A

Question. If 3x = cosec q and 3 x = cot q, the value of 3 (x2– 1/x2) is
(a) 1/ 2
(b) 1/ 4
(c) 1/ 3
(d) 1/ 5

C

Question. If cos θ + sin θ = 2 cos θ, then cos θ– sin θ equals
(a) sin θ
(b) 2 sin θ
(c) √2 sin θ
(d) sin θ/ 2

C

Question. If x = r sin θ cos Φ, y = r sin θ sin Φ, z = r cos θ, then x2 + y2 + z2 =
(a) r
(b) r2
(c) 2r
(d) r 2

B

Question. The value of cot2 θ – 1/sin2θ is
(a) 0
(b) –1
(c) 2
(d) –8

B

Question. If cosec θ + cot θ = x, the value of cosec θ – cot θ is
(a) x
(b) 2x
(c) x/ 2
(d) 1/ x

D

Question. If sin A + sin2 A = 1, then the value of the expression (cos2 A + cos4 A) is
(a) 0
(b) 1
(c) 2
(d) 9

B

Question. Simplest form of 1+ tan2 A/1 +cot2 A is
(a) sin2 A
(b) cos2 A
(c) sec2 A
(d) tan2 A

D

Question. The magnitude of θ in the equation cos2θ/cot2θ – cos2θ =3 is
(a) 0°
(b) 30°
(c) 60°
(d) 90°

C

Question. The value of tan tan2θ /1+ tan2θ + cot2θ/1 + cot2θ is equal to
(a) 1
(b) 2
(c) 3
(d) None of these

A

Question. The value of (cosec2θ–1) tan2θ is
(a) 0
(b) 1
(c) 2
(d) 7

B

Question. The value of (1 + cot θ – cosec θ) (1 + tan θ + sec θ) is equal to
(a) 1
(b) 2
(c) 3
(d) 4

B

Question. If 4 tan θ = 3, then [4sin θ – cos θ /4sin θ + cosθ] is equal to
(a) 2/ 3
(b) 1/ 3
(c) 1/ 2
(d) 3 /4

C

Question. If 7 sin2A + 3 cos2A = 4, then tan A =
(a) 1/ 2
(b) 1 /3
(c) 1 /2
(d) 1/ 3

D

Question. The value of (1 + tan2 θ)(1 – sin θ)(1 + sin θ) is
(a) 0
(b) 1
(c) 8
(d) 17

B

Question. If x = 2 sin2 θ, y = 2 cos2 θ + 1, then the value of x + y is
(a) 1
(b) 2
(c) 3
(d) 12

C

Question. If tan (A + B) = 1 and tan (A – B) = 1/√3 . 0° < A + B < 90°. A > B, then the values of A and B respectively are
(a) A = 30°, B = 4.5°
(b) A = 37.5°, B = 7.5°
(c) A = 15°, B = 30°
(d) None of these

B

Question. If sin θ – cos θ = 0, then the value of (sinθ + cos4 θ) is
(a) 1
(b) 3 /4
(c) 1/ 2
(d) 1/ 4

C

Question. If sec θ + tan θ = p, then the value of cosec θ is
(a) p2 – 1/p2 +1,-1
(b) p2 -1/p2 +1,1
(c) p2 + 1/p2 +2, -1
(d) None of these

A

Question. If 2 sin θ = √3 , then θ =
(a) 30°
(b) 60°
(c) 45°
(d) 90°

B

Question. In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
1. Assertion (A): sin2 67° + cos2 67° = 1.
Reason (R): For any value of q, sin2 θ + cos2 θ = 1.
2. Assertion (A): The value of sec2 10° – cot2 80° is 1.
Reason (R): The value of sin 30° = 1/ 2

1. (A) ,2. (B)

One Word Questions :

Question. In Fig. 3 ABCD is a rectangle, find AE.

80

Question. If sin2A = cos3A , then find the value of A.

18

Question. In the figure, find the area of ΔABC is which ∠ACB = 450 and BC=8cm.

32cm2

Question. Name the angle of depression in the figure.

∠ABC

Question. If x = 3sec2θ −1 and y = 3tan2θ − 2 then find the value of x – y.

4

Question. If 2x = cos ecθ and 2/x = cot2 , then find the value of 4(x2 – 1/x2) .

1

Question. Find the value of cosec39°/sec 51° + 2(sin2 5° + sin2 85°).

3

Question. If tan tan(90 ) 0 , then find the value of θ

45°

Question. Complete the following:-
The angle nearer to altitude is ____________ than the angle away from the altitude.

greater

Question. Find the value of cos2 150 + cos2 250 + cos2 650 + cos2 750

2

Question. Find the value of tan100 tan 200 tan 700 tan 800

0

Question. In Fig. 4 find the value of CF.

12

Question. If cos20°/sin70° 2cos/sin(90°) k/2 , then find the value of k.

6

Question. If tan 4θ = cotθ , where 4θ and θ and are acute angles, then find the value of θ .

18°

Question. If cos (81°+ θ) = sin (k/3 – θ) , then find the value of k.

27

Question. Find the value of sin2 100 + sin2 800

1

Question. Find the value of sin2 100 + sin2 800

1

Question. If SecA 3/2 , then find the value of tan2 A .

5/4

Question. Find the value of cos2 670 − sin2 230