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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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°

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

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

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

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

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

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

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

Question. Trigonometry deals with measurement of components of triangles.       

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

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

Question. sin2 A = (sin A)²       

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

Question. The value of cos90° is 1.       

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

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

Question. sin(90° – A) = cos A       

Question. cos(90°-A)= sec A       

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

Question. (1 -cos²θ)sec²θ = tanθ       

Question. tanq increases faster than sinq as q increases.       

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

Question. tan70°tan20° =1       

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

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

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

Question. How is cotΘ expressed in terms of sinΘ ?

Question. Find the value of the expression sin² 22^o + sin² 68o / coso22^o + cos² 68⁰ + sin63 + cos63 sin 27^o
(a) 3
(b) 2
(c) 1
(d) 0

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

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

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

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

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

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

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

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

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

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

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

Question. What is the value of sin0^o + cos30^o – tan45^o + cosec 60^o + cot90^o ?
(a) 7√3 – 6 / 6
(b) 6 + 7√3 / 6
(c) 0
(d) 2

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

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

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

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

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

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

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

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

(a) 1/2
(b) 1/√2
(c) 1/4
(d) 1/8

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

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

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

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) 36.8^o
(b) 68^o
(c) 38^o
(d) 60^o

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question. If sin θ – cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is
(a) 1
(b) 3 /4
(c) 1/ 2
(d) 1/ 4

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

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

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

One Word Questions :

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

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

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

Question. Name the angle of depression in the figure.

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

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

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

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

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

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

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

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

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

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

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

Question. Find the value of sin² 10⁰ + sin² 80⁰

Question. Find the value of sin² 10⁰ + sin² 80⁰

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

Question. Find the value of cos² 67⁰ − sin² 23⁰

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