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 to Trigonometry 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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°

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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°

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

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 + y_²+ z2 = r²
(d) z2 + y2 – x2 = r²

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fill in the Blanks :

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

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

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

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

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

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

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

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

Question. sin² A + cos² A = ………….. 

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

True or False :

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

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

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

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

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

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

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

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

Match the Following :

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

Column-I	Column-II
(A) sin C	(p) 3/5
(B) cos C	(q) 4/5
(C) tan A	(r) 5/3
(D) sec A	(s) 4/3

Question . If sin A = 7/ 25 , then

Column-I	Column-II
(A) cos A	(p) 24/25
(B) tan A	(q) 7/24
(C) cosec A	(r) 25/7
(D) sec A	(s) 25/24

We hope the above multiple choice questions for Class 10 Mathematics for Chapter 8 Introduction to Trigonometry provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Introduction to Trigonometry is an important chapter in Class 10 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 10 students. Please go through these and let us know if you have any feedback in the comments section.