MCQ Questions for Class 10 Trigonometry

MCQs MCQs Class 10

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

Answer

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

Answer

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

Answer

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

Answer

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°

Answer

D

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

Answer

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

Answer

B

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

Answer

C

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

Answer

C

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

Answer

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

Answer

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

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. 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

Answer

C

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

Answer

C

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

Answer

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) ∝

Answer

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

Answer

C

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

Answer

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

Answer

B

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

MCQ Questions for Class 10 Trigonometry

(a) √2/√3
(b) 1/3
(c) 1/2
(d) 1/√3

Answer

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

Answer

A

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

MCQ Questions for Class 10 Trigonometry

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

Answer

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

Answer

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°

Answer

D

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

Answer

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

Answer

C

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

Answer

A

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

Answer

D

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

Answer

B

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

Answer

F

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

Answer

T

Question. Trigonometry deals with measurement of components of triangles.       

Answer

T

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

Answer

T

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

Answer

F

Question. sin2 A = (sin A)2       

Answer

T

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

Answer

T

Question. The value of cos90° is 1.       

Answer

F

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

Answer

T

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

Answer

F

Question. sin(90° – A) = cos A       

Answer

T

Question. cos(90°-A)= sec A       

Answer

F

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

Answer

F

Question. (1 -cos2θ)sec2θ = tanθ       

Answer

T

Question. tanq increases faster than sinq as q increases.       

Answer

T

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

Answer

F

Question. tan70°tan20° =1       

Answer

T

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

Answer

T

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

Answer

F

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

Answer

F

Question. How is cotΘ expressed in terms of sinΘ ?

MCQ Questions For Class 10 Introduction to Trigonometry
Answer

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

Answer

B

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

Answer

A

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

Answer

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

Answer

B

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

Answer

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

Answer

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

Answer

D

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

MCQ Questions For Class 10 Introduction to Trigonometry

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

Answer

C

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

Answer

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

Answer

C

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

A

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

Answer

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

Answer

D

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

MCQ Questions For Class 10 Introduction to Trigonometry

(a) 1/2
(b) 1/√2
(c) 1/4
(d) 1/8

Answer

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

Answer

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) ∝

Answer

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

Answer

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

Answer

A

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

Answer

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

Answer

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

Answer

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

Answer

B

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

Answer

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

Answer

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

Answer

B

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

Answer

D

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

Answer

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

Answer

A

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

Answer

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

Answer

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

Answer

C

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

Answer

D

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

A

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

Answer

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

Answer

1. (A) ,2. (B)

One Word Questions :

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

Answer

80

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

Answer

18

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

MCQ Questions for Class 10 Trigonometry
Answer

32cm2

Question. Name the angle of depression in the figure.

MCQ Questions for Class 10 Trigonometry
Answer

∠ABC

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

Answer

4

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

Answer

1

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

Answer

3

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

Answer

45°

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

Answer

greater

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

Answer

2

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

Answer

0

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

MCQ Questions for Class 10 Trigonometry
Answer

12

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

Answer

6

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

Answer

18°

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

Answer

27

Question. Find the value of sin2 100 + sin2 800

Answer

1

Question. Find the value of sin2 100 + sin2 800

Answer

1

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

Answer

5/4

Question. Find the value of cos2 670 − sin2 230

Answer

0

Question. If x = sin2θ and y = cos2θ +1 , then find the value of x+y.

Answer

2

mcq questions for class 10 maths Trigonometry with answers