# Unseen Passage

For Class 4 to Class 12

# Trigonometry MCQ Class 10 Mathematics

Please refer to Chapter 8 Trigonometry MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Trigonometry and then attempt the following objective questions.

## MCQ Questions Class 10 Mathematics Chapter 8 Trigonometry

The Trigonometry MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. If 6cot θ + 2cosec θ = cot θ + 5cosec θ, then cos θ is
(a) 4/5
(b) 5/3
(c) 3/5
(d) 5 /4

C

Question. If tan A =3/2 then the value of cos A is
(a) 3/√13
(b) 2/√13
(c) 2/3
(d) √13/2

B

Question. The value of 2tan30°/1- tan230° 2 is equal to
(a) cos 60°
(b) sin 60°
(c) tan 60°
(d) sin 30°

C

Question. If sin θ = 7√85 , what are the values of tan θ, cos θ and cosec θ?
(a) tanθ=6/7 , cosθ=7/√85 and cosecθ=√85/7
(b) tanθ= 7/6, cosθ=7/√85 and cosecθ=√85/7
(c) tanθ=7/6 , cosθ=6/√85 and cosecθ=√85/7
(d) tanθ=7/6 , cosθ=6/√85 and cosecθ=√85/6

C

Question. Given that sinθ a/b, then cos θ is equal to
(a) b/√b2-a2
(b) b/a
(c) √b2-a2/b
(d) a/√b2-a2

C

Question.Consider the triangle shown below.

What are the values of tan θ, cosec θ and sec θ?
(a) tanθ=8/15 , cosecθ=17/8 , secθ=17/15
(b) tanθ=8/15 , cosecθ=17/15 , secθ=17/8
(c) tanθ=17/15 , cosecθ=8/15 , secθ=17/8
(d) tanθ=8/15 , cosecθ=17/15 , secθ=8/17

A

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

A

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

C

Question. Value of sin 30° tan 45° is
(a) √3/2
(b) 2
(c) 1/2
(d) 0

C

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

B

Question. The value of tan260º-sin230º/tan245°+cos230° is
(a) 7/11
(b) 11/13
(c) 13/11
(d) 11/7

D

Question. If x = r sin θ and y = r cos θ then the value of x2 + y2 is
(a) r
(b) r2
(c) 1/r
(d) 1

B

Question. If 3 sec θ – 5= 0 then cot i is equal to
(a) 5/3
(b) 4/5
(c) 3/4
(d) 3/5

C

Question. If α+β = 90° and α = 2β, then cos2α+ sin2β  is equal to
(a) 1
(b) 1/2
(c) 0
(d) 2

B

Question. If sin A=1/2, then the value of cot A is
(a) √3
(b) 1/√3
(c) √3/2
(d) 1

A

Question. If tan x sin x m and tan x – sin x= n then m2 – n2 is equal to
(a) 4 √mn
(b) √mn
(c) 2 √mn
(d) none of them

A

Question. 1+tan2A/1+cot2A is equal to
(a) sec2A
(b) –1
(c) cot2 A
(d) tan2 A

D

Question. sinθ/1-cosθ+cosθ/1-tanθ is equal to
(a) 0
(b) 1
(c) sinθ+cos θ
(d) sinθ – cosθ

C

Question. Given that sin , then tan b a i = i is equal to
(a) b/√b2-a2
(b) √b2-a2/b
(c) a/√b2-a2
(d) √b2-a2/a

C

Question. Considering the diagram below.

Which of the following statements is true?
(a) Side PR is adjacent to ∠y in triangle PMR and side QR is adjacent to ∠y in triangle PQR
(b) Side MR is adjacent to ∠y in triangle PMR and side PR is adjacent to ∠y in triangle PQR
(c) Side PR is adjacent to ∠y in triangle PMR and side MR is adjacent to ∠y in triangle PQR
(d) Side PR is adjacent to ∠y in triangle PMR and triangle PQR

B

Question. The two legs AB and BC of right triangle ABC are in a ratio 1 : 3. What will be the value of sin C?
(a) √10
(b) 1/√10
(c) 3/√10
(d) 1/2

B

Question. The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) is
(a) – 1
(b) 0
(c) 1
(d) 2

B

Question. The value o tan30 °/ cot60° is
(a) 1/√2
(b) 1/√3
(c) √3
(d) 1

D

Question. The value of 4-sin245° /cot k tan60º  is 3.5.
What is the value of k?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

C

Question. Which of these is equivalent to 2tanx(sec2x-1)/cos3x  ?
(a) 2 tan3 x cosec x
(b) 2 cot3 x cosec3 x
(c) 2 tan3 x sec3 x
(d) 2 cot3 x sec3 x

C

Question. If sin θ + cos θ = √2 cos θ, (θ ≠ 90) then the value of tan θ is
(a) √2 – 1
(b) √2 +1
(c) √2
(d) – √2

A

Question. Which of the following option makes the statement below true?
1/secx+secx/cos2 x-1-tan2 x
(a) −cosec x tan x
(b) −sec x tan x
(c) −cosec x cot x
(d) −sec x cot x

C

Question. If sec i+tan i = x, the value of sec i is
(a) 1/2(x-1/x)
(b) x2-1/x2+1
(c) 1/2(x+1/x)
(d) none of them

C

Question. If sinθ= 1/3, the value of (2cot2 θ + 2) is
(a) 16
(b) 20
(c) 12
(d) 18

D

Question. (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) is equal to
(a) 0
(b) 1
(c) –1
(d) none of these

B

Question. (sec A + tan A) (1 – sin A) is equal to
(a) sec A
(b) sin A
(c) cosec A
(d) cos A

D

Question. The value of √1+cosθ/1-cosθ
(a) cotθ– cosecθ
(b) cosecθ+cotθ
(c) cosec2θ+ cot2θ
(d) (cotθ+ cosecθ )2

B

Question. Given that sinα= 1/2 and cos β=1/2, then the value of (a + b) is
(a) 0°
(b) 30°
(c) 60°
(d) 90°

D

Question. The value of (1 + cot θ – cosec θ)(1 + tan θ + sec θ) is
(a) 1
(b) 2
(c) –1
(d) None of these

B

Question. If sin 77° = x, than the value of tan 77° is
(a) 1/1+x2
(b) x/√1+x2
(c) x/√1-x2
(d) None of these

C

Question. sec4 A – sec2 A is equal to
(a) tan2A – tan4A
(b) tan4A – tan2A
(c) tan4A + tan2A
(d) None of these

C

Question. If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then a2 + b2 is equal to
(a) m2 – n2
(b) m2n2
(c) n2 – m2
(d) m2 + n2

D

Question. If x = a cos θ and y = b sin θ, then the value of b2x2 + a2y2 is
(a) a2 + b2
(b) a2/b2
(c) a2b2
(d) None of these

C

Question. If √3 tan θ = 3 sin θ, (θ ≠ 0) then the value of sin2 θ – cos2 θ is
(a) 1/3
(b) 3
(c) 2/3
(d) 3/2

A

Question. If cos A + cos2A = 1, then sin2A + sin4A is equal to
(a) –1
(b) 0
(c) 1
(d) None of these

C

Question. The value of (sin 45° + cos 45°) is
(a) 1/√2
(b) √2
(c) √3/2
(d) 1

B

Question. What is the value of 3-sin260º/tan30ºtan60º  ?
(a) 21/4
(b) 31/4
(c) 2 3/4
(d) 3 3/4

A

Question. If 4 tan x = 3, than cos x +sin x/cos x-sin x is equal to
(a) 7
(b) 1/7
(c) – 7
(d) –1/7

A

Question. cos4 A – sin4 A is equal to
(a) 2cos2A + 1
(b) 2cos2A – 1
(c) 2sin2A – 1
(d) 2sin2 A + 1

B

Question. sinθ/1+cosθ is equal to
(a) 1+cosθ/sinθ
(b) 1+cosθ/cosθ
(c) 1-cosθ/sinθ
(d) 1-sinθ/cosθ

C

Question. The value of the expression sin 60°/cos30º  is
(a) √3/2
(b) 1/2
(c) 1
(d) 2

C

Question. If 2x = sec θ and tan 2/x = tanθ , then the value of (x2-1/x2) is
(a) 4
(b) 1/4
(c) 2
(d) 1/2

B

Question. Value of cos 0° ⋅ cos 30° ⋅ cos 45° ⋅ cos 60° ⋅ cos 90° is
(a) 0
(b) 1
(c) 2
(d) 9

A

Question. ABC is a triangle right angled at C and AC = √3 BC. Then ∠ABC =
(a) 30°
(b) 60°
(c) 90°
(d) 0°

B

Question. The value of sin 60° ⋅ cos 30° + sin 30° ⋅ cos 60° is
(a) 0
(b) 1
(c) 2
(d) 8

B

Question. If sin (A + B) = √3/2 and sin 2B = 1/ 2 , then
(a) tan B = 1
(b) B = 30°
(c) B = 45°
(d) cosA 1/ 2

C

Question. If x = a (cosec θ + cot θ) and y = b(1 cos )/ sinθ − , then xy =
(a) a2 + b2/ a2– b
(b) a2 – b2
(c) ab
(d) a b

C

Question. If x = p sec q and y = q tan θ , then
(a) x2 – y2 = p2q2
(b) x2q2 – y2p2 = pq
(c) x2q2 – y2p2 = 1/p2q2
(d) x2q2 – y2p2 = p2q2

D

Question. If p sin θ + q cos θ = a and p cos θ – q sin θ = b, then p+a/q+b + q-b/p-a =
(a) 1
(b) a2 + b2
(c) 0
(d) 2

C

Question. If cosec A + cot A = 11/ 2 , then tan A
(a) 21/ 22
(b) 15/ 16
(c) 44 /117
(d) 11 /117

C

Question. 2tan30°/1+ tan 30 ° + ° is equal to
(a) sin 30°
(b) cos 60°
(c) 1/ 2
(d) √3/2

D

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

A

Question. If tan2θ = 1– a2, then the value of sec θ + tan3θ cosec θ is
(a) (2 – a2)
(b) (2 – a2)1/2
(c) (2 – a2)2/3
(d) (2 – a2)3/2

D

Question. If x = a cos2θ + b sin2θ, then (x – a) (b – x) is equal to
(a) (a – b) sinθ cosθ
(b) (a – b)2 sin2θ cos2θ
(c) (a – b)2 sinθ cosθ
(d) (a – b) sin2θ cos2θ

B

Question. If cos A = 3/ 5 , find the value of 9 cot2A – 1.
(a) 1
(b) 16/ 65
(c) 65 /16
(d) 0

C

Question. 2tan30°/ 1+ tan230 ° =
(a) sin 60°
(b) cos 60°
(c) tan 60°
(d) sin 30°

A

Question. 9 sec2 A – 9 tan2 A =
(a) 1
(b) 9
(c) 8
(d) 0

B

Question. cos 1° . cos 2°. cos 3° ……… cos 179° is equal to
(a) –1
(b) 0
(c) 1
(d) 1/√2

B

Question. If (sec2θ) (1 + sinθ) (1 – sinθ) = k, then find the value of k.
(a) sinθ
(b) secθ
(c) 1
(d) cotθ

C

Question. sin2q + cosec2q is always
(a) greater than 1
(b) less than 1
(c) greater than or equal to 2
(d) equal to 2

C

Question. sin 2A = 2 sin A is true when A =
(a) 0°
(b) 30°
(c) 45°
(d) 60°

A

Question. If b tan θ = a, the value of  asinθ-bcosθ/asinθ + bcosθ  is
(a) a – b/a2 + b
(b) a + b/ a2 + b2
(c) a2 + b2/ a2– b
(d) a2– b2/ a2 + b

D

Question. (cos4A – sin4A) is equal to
(a) 1 – 2 cos2A
(b) 2 sin2 A – 1
(c) sin2A – cos2A
(d) 2 cos2A – 1

D

Question. If cosθ/1-sinθ + cosθ/1+sinθ= 4, then
(a) cosθ =√3 /2
(b) sinθ = 1/ 2
(c) θ = 60°
(d) tanθ = 1/√3

C

Question. 2 tan30°/ 1- tan2 30° =
(a) cos 60°
(b) sin 60°
(c) tan 60°
(d) sin 30°