# MCQs for Mathematics Class 10 with Answers Chapter 8 Introduction to Trigonometry

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Introduction to Trigonometry with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

## Chapter 8 Introduction toTrigonometry MCQ with Answers Class 10 Mathematics

MCQ Questions Class 10 Mathematics Introduction to Trigonometry provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. The value of cos θ cos(90° – θ) – sin θ sin (90° – θ) is:
(a) 1
(b) 0
(c) -1
(d) 2

B

Question. If x and y are complementary angles, then
(a) sin x = sin y
(b) tan x = tan y
(c) cos x = cos y
(d) sec x = cosec y

D

Question. If cos 9a = sin a and 9a < 90°, then the value of tan 5a is
(a) 1/√3
(b) √3
(c) 1
(d) 0

C

Question. If sin θ = cos4θ, then the value of θ is :
(a) 18°
(b) 36°
(c) 45°
(d) none of these

A

Question. The value of sec cosec (90º ) tan cot (90º ) (sin2 35 sin2 55º )/ tan10º tan 20º tan 45º tan 70º tan 80º  is
(a) 1
(b) –1
(c) 2
(d) 3

C

Question. The value of (sin 35°/ cos55°)2 + (cos55°/ sin 35°)2−2cos60°  is :
(a) 0
(b) 1
(c) –1
(d) 2

B

Question. (cosec A – sin A) (sec A – cos A) (tan A + cot A) is equal to :
(a) 1
(b) –1
(c) 2
(d) –2

A

Question. 7 sin 2 θ + 3 cos 2 θ = 4 then :
(a) tan θ =1/√2
(b) tan θ =1/2
(c) tan θ =1/3
(d) tan θ =1/√3

D

Question. (1 + tanθ + secθ) (1 + cotθ – cosecθ) is equal to
(a) 0
(b) 1
(c) 2
(d) -1

C

Question. If cos (α + β) = 0, then sin (α – β) can be reduced to
(a) cos β
(b) cos 2β
(c) sin α
(d) sin 2α

B

Question. If tan θ =12/5 , then 1+sinθ/1- sinθ is equal to
(a) 24
(b) 12/13
(c) 25
(d) 9

C

Question. The value of sin 75º− sin15º/ cos15º− cos75º  is :
(a) 0
(b) –1
(c) 1
(d) none of these

C

Question. √cosec θ + 1 -/ cosec θ – 1 +√ cosec θ – 1 cosec θ + 1  is equal to :
(a) cos θ
(b) 2 cos θ
(c) 1/ cos θ
(d) 2/ cos θ

D

Question. In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is
(a) 0
(b) 1
(c) – 1
(d) 2

B

Question. Given that sin A= and cos B=1/√2 then the value of (A + B) is:
(a) 30°
(b) 45°
(c) 75°
(d) 15°

C

Question. If cos (40° + A) = sin 30°, the value of A is:?
(a) 60°
(b) 20°
(c) 40°
(d) 30°

B

Question. If sin x + cosec x = 2, then sin19  x + cosec 20 x =
(a) 2 19
(b) 2 20
(c) 2
(d) 2 39

C

Question. Given sinθ + cosθ = √3 , what is the value of tanθ + cotθ .
(a) 1/√2
(b) 2/√3
(c) √3/2
(d) 1

D

Question. C is the centre of a circle of radius 3 units, and θ is the angle as shown in the given figure. If sin θ + cos θ = x2 + 1/x2 , ,find the value of x.

(a) 2
(b) 4
(c) 6
(d) 8

A

Question. If x = a secθ + b tanθ and y = b secθ + a tanθ , find x2 – y2 .
(a) 4a bsecθ + a tanθ
(b) a2 – b2
(c) b2 – a2
(d) a2 + b2

B

Question. Find the value of cos30° cos45° – sin30° sin45° .
(a) √6 + 1/2
(b) √6 + √2/4
(c) √6 – √2/8
(d) √2(√3 – 1)/4

D

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

D

Question. If tan x = sin 45°cos 45° + sin30° , find the value of x .
(a) 30°
(b) 60°
(c) 45°
(d) 90°

C

Question. Find the value sin2 30° cos2 45° + 4tan2 30° + 1/2 sin2 90° – 2cos2 90° + 1/24 .
(a) 1
(b) 2
(c) √2
(d) √3

B

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

C

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

C

Question. Find the value of cos1° cos2° cos3° …..cos89° cos90° .
(a) 1
(b) 1/2
(c) 1/√2
(d) 0

D

Question. Ratios of sides of a right triangle with respect to its acute angles are known as
(a) trigonometric identities
(b) trigonometry
(c) trigonometric ratios of the angles
(d) none of these

C

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

A

Question. If sin θ − cos θ = 0, vthen the value of θ is
(a) 90°
(b) 30°
(c) 45°
(d) 60°

C

Question. sin (45° + θ) – cos (45° – θ) is equal to
(a) 2 cos θ
(b) 0
(c) 2 sin θ
(d) 1

B

Question. If 0° < θ < 90°, then sec 0 is
(a) >1
(b) < 1
(c) =1
(d) 0

A

Question. If tan 2A = cot (A – 18°), then the value of A is
(a) 24°
(b) 18°
(c) 27°
(d) 36°

D

Question. If cos A + cos2 A = 1, then sin2 A + sin 4 A is
(a) -1
(b) 0
(c) 1
(d) 2

C

Question. If sin θ + sin 2 θ = 1, then cos 2 θ + cos 4 θ = ____
(a) -1
(b) 0
(c) 1
(d) 2

C

Question. If 3 tan θ = 4, then the value of √1- sinθ /1+ sinθ  is :
(a) 1
(b) 1 2
(c) 1 3
(d) 2 3

C

Question. If 5 sin θ – 3 = 0, then the value of cosecθ- cotθ/ 2cotθ  is :
(a) 1/ 4
(b) 1/ 8
(c) 3/ 4
(d) 7/ 8

B

Question. sin 2B = 2 sin B is true when B is equal to
(a) 90°
(b) 60°
(c) 30°
(d) 0°

D

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

B

Question. If 5tan θ − 4 = 0 , then the value of 5sinθ – 3cosθ 5sinθ + 2cosθ is
(a) 2 /3
(b) 1/ 3
(c) 1/ 6
(d) 5/ 2

C

Question. If sin 4/5 , then the value of 4 tanθ− 5cosθ/ secθ +cotθ  is
(a) 1
(b) 5 /8
(c) 7/ 4
(d) 28/ 29

D

Question. The value of 4 (sin4 30° + cos4 30°) – 3 (sin2 45° – 2 cos2 45°) is
(a) 0
(b) 1
(c) 4
(d) none of these

C

Question. If √3tanθ = 3sinθ, then the value of sin 2 θ−cos 2 θ is
(a) 0
(b) 1
(c) 1/2
(d) 1/3

D

Question. Out of the following options, the two angles that are together classified as complementary anglesare
(a) 120° and 60°
(b) 50° and 30°
(c) 65° and 25°
(d) 70° and 30°

C

Question. The value of sin2 63°+ sin27°/ cos2 17°/ cos2 73°  is
(a) 0
(b) 1
(c) 2
(d) none of these

B

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

A

Question. If a cot θ + b cosec θ = p and b cot = + a cosec θ = q, then p2 – q2 is equal to :
(a) a2 – b2
(b) b2 – a2
(c) a2 + b2
(d) a + b

B

Question. If (1 + cos α) (1 + cos β) (1 + cos ϒ) = (1 – cos α) (1 – cos β) (1 – cos ϒ), then each of the expression is equal to :
(a) sin α sin β sin ϒ
(b) cos α cos β cos ϒ
(c) ± sin α sin β sin ϒ
(d) ± cos α cos β cos ϒ

C

Question. The value of tan 5° tan 10° tan 15° tan 75° tan 80° tan 85° is :
(a) –1
(b) 0
(c) 1
(d) none of these

C

Question. The value of 4 cot245° – sec260° + sin260° + cos290° is
(a) 1/ 4
(b) 2/ 4
(c) 3 /4
(d) 1

C

Question. If tan 3x = sin 45° cos 45° + sin 30°, then the value of x is :
(a) 15°
(b) 30°
(c) 45°
(d) 60°

A

Question. The value of sin 75°/cos15°+  sin12°/cos78°− cos18°cosec72° is :sin12°
(a) –1
(b) 0
(c) 1
(d) none of these

C

Question. tanθ – cotθ/ sinθ cosθ is equal to
(a) sec2 θ + cosec2 θ
(b) cot2 θ – tan2 θ
(c) cos2 θ – sin2 θ
(d) tan2θ – cot2θ

D

Question. If cosec x – cot x = 1 3 , where x ≠ 0, then the value of cos2x – sin2x is
(a) 16/ 25
(b) 9 /25
(c) 8 /25
(d) 7 /25

D

Question. If tan2q = 1 – e2, then the value of secq + tan3q cosec q is equal to
(a) (1 – e2)1/2
(b) (2 – e2)1/2
(c) (2 – e2)3/2
(d) (1 – e2)3/2

C

Question. If sinq + sin3q = cos2q, then the value of cos6q – 4cos4q + 8cos2q is
(a) 1
(b) 4
(c) 2
(d) 0

B

Question. If cot θ =(15/8) , then evaluate (2+ 2sin ) (1- sin )/ (1+ cos ) (2 – 2cos )
(a) 1
(b) 225/ 64
(c) 156/7
(d) –1

B

Question. If sin A + sin2A = 1, then the value of the expression (cos2A + cos4A) is
(a) 1
(b) 1/ 2
(c) 2
(d) 3

A

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. sinθ – 2sin3θ/ 2cos3θ – cos θ is equal to
(a) sec θ
(b) tan θ
(c) √sec θ −1
(d) cot θ

B

Question. (1 + tan θ + sec θ) (1 + cot θ– cosec θ) =
(a) 0
(b) 1
(c) 2
(d) –1

C

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

D

Question. 1+ tan2 A/1 + cot2 A + =L
(a) sec2 A
(b) –1
(c) cot2 A
(d) tan2 A

D

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 of tan 30°/ cot 60°  is
(a) 1/√2
(b) 1/√3
(c) √3
(d) 1

D

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

B

Question. 1- tan245°/ 1+ tan2 45° =
(a) tan 90°
(b) 1
(c) sin 45°
(d) 0

D

Fill in the Blanks :

Question. In a right trianlge ABC, right angled at B, if tan A = 1, sin A cos A = ……….

1/ 2

Question. The value of sin A or cos A never exceeds ……

1

Question. If tan A = 4/3, then sin A ……………

4/5

Question. In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of tan P is ………..

12/5

Question. If 15 cot A = 8, sec A = …………..

17/8

Question. 2 tan2 45° + 3 cos2 30° – sin2 60° = ………….

7/ 2

Question. In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. sin A = ………..

7/25

Question. sin 60° cos 30° + sin 30° cos60° = …………….

1

Question. sin2 A + cos2 A = …………..

1

Question. cos45°/ sec30 °+ cosec 30 ° =  …………..

3(√3 1) /4

True or False :

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

True

Question. cot A is the product of cot and A.

False

Question. The value of tan A is always less than 1.

False

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

False

Question. sinθ = 4/ 3  , for some angle θ.

False

Question. sin (A + B) = sin A + sin B. False

False

Question. sec A = 12/5, for some value of angle A.

True

Question. If ∠B and ∠Q are acute angles such that sin B = sin Q, then ∠B ≠ ∠Q.

False

Match the Following :

Question . In Δ ABC, ∠ B = 90°, AB = 3 cm and BC = 4 cm, then match the column.

(A) → p; (B) → q; (C) → s; (D) → r

Question . If sin A = 7/ 25 , then