CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 22

Practice MCQs for Class 10 Mathematics Chapter 08 Introduction to Trigonometry

Review structured MCQ sets for Class 10 Mathematics Chapter 08 Introduction to Trigonometry. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Access Chapter 08 Introduction to Trigonometry Questions and Solutions

Navigate directly to the 50 objective questions for Chapter 08 Introduction to Trigonometry using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: If sin α = 1/√2 and tan β = 1, where α and β are acute, then sin(α + β) equals
(a) 0
(b) 1/√2
(c) √3/2
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. sin α = 1/√2 gives α = 45° and tan β = 1 gives β = 45°. So sin(α + β) = sin 90° = 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 2: If cos α = 1/2 and tan β = 1/√3, where α and β are acute, then sin(α + β) equals
(a) 1/2
(b) √3/2
(c) 0
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. cos α = 1/2 gives α = 60° and tan β = 1/√3 gives β = 30°. So sin(α + β) = sin 90° = 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 3: The value of sin 20° / cos 70° is
(a) 0
(b) 1/2
(c) sin 20°
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. cos 70° = sin(90° − 70°) = sin 20°, so the ratio is 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 4: The value of tan 10° / cot 80° is
(a) 0
(b) 1
(c) tan 80°
(d) 1/2
Show Answer & Explanation

Answer: (b) 1

Explanation:
1. cot 80° = tan(90° − 80°) = tan 10°, so the ratio is 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 5: The value of (sin 49° / cos 41°)² + (cos 41° / sin 49°)² is
(a) 1
(b) 0
(c) 4
(d) 2
Show Answer & Explanation

Answer: (d) 2

Explanation:
1. cos 41° = sin 49°, so each fraction equals 1. The sum is 1 + 1 = 2.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 6: The value of cot 40° / tan 50° − (1/2)(cot 35° / tan 55°) is
(a) 0
(b) 1/2
(c) 1
(d) 3/2
Show Answer & Explanation

Answer: (b) 1/2

Explanation:
1. cot 40° = tan 50° and cot 35° = tan 55°, so each fraction is 1. The value is 1 − 1/2 = 1/2.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 7: The value of cosec² 67° − tan² 23° is
(a) 0
(b) 2
(c) −1
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. cosec 67° = sec 23°. So the value is sec² 23° − tan² 23° = 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 8: The value of sin² 20° + sin² 70° − tan² 45° is
(a) 1
(b) 2
(c) 0
(d) −1
Show Answer & Explanation

Answer: (c) 0

Explanation:
1. sin 70° = cos 20°, so sin² 20° + cos² 20° = 1. Also tan 45° = 1, so the value is 1 − 1 = 0.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 9: The value of sec 50° sin 40° + cos 40° cosec 50° is
(a) 1
(b) 2
(c) 0
(d) √2
Show Answer & Explanation

Answer: (b) 2

Explanation:
1. sec 50° = 1/cos 50° = 1/sin 40°, so sec 50° sin 40° = 1. Similarly cosec 50° = 1/sin 50° = 1/cos 40°, so cos 40° cosec 50° = 1. The sum is 2.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 10: The value of sin 48° sec 42° + cos 48° cosec 42° is
(a) 2
(b) 1
(c) 0
(d) √3
Show Answer & Explanation

Answer: (a) 2

Explanation:
1. sec 42° = cosec 48° and cosec 42° = sec 48°. So sin 48° sec 42° = 1 and cos 48° cosec 42° = 1, giving 2.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 11: The value of sin 63° cos 27° + cos 63° sin 27° is
(a) 0
(b) 1/2
(c) 2
(d) 1
Show Answer & Explanation

Answer: (d) 1

Explanation:
1. cos 27° = sin 63° and sin 27° = cos 63°. So the expression is sin² 63° + cos² 63° = 1.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 12: The value of cos 80° / sin 10° + cos 59° cosec 31° is
(a) 1
(b) 0
(c) 3
(d) 2
Show Answer & Explanation

Answer: (d) 2

Explanation:
1. cos 80° = sin 10°, so the first term is 1. cosec 31° = 1/sin 31° = 1/cos 59°, so cos 59° cosec 31° = 1. The sum is 2.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 13: If tan θ = 8/15 and 0° < θ < 90°, then sin θ equals
(a) 8/17
(b) 15/17
(c) 8/15
(d) 17/8
Show Answer & Explanation

Answer: (a) 8/17

Explanation:
1. With opposite = 8 and adjacent = 15, hypotenuse = √(64 + 225) = 17. So sin θ = 8/17.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 14: If sin θ = 8/17 and 0° < θ < 90°, then tan θ equals
(a) 8/15
(b) 15/8
(c) 8/17
(d) 15/17
Show Answer & Explanation

Answer: (a) 8/15

Explanation:
1. opposite = 8, hypotenuse = 17, so adjacent = √(289 − 64) = 15. Hence tan θ = 8/15.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 15: If sin A = 24/25, then tan A + sec A (0° < A < 90°) equals
(a) 7
(b) 24/7
(c) 25/7
(d) 1/7
Show Answer & Explanation

Answer: (a) 7

Explanation:
1. opposite = 24, hypotenuse = 25, adjacent = 7. So tan A + sec A = 24/7 + 25/7 = 49/7 = 7.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 16: If tan θ = 3/4, then (1 − cos θ)/(1 + cos θ) equals
(a) 1/7
(b) 1/9
(c) 1/3
(d) 9
Show Answer & Explanation

Answer: (b) 1/9

Explanation:
1. tan θ = 3/4 gives cos θ = 4/5 (3-4-5 triangle). So (1 − 4/5)/(1 + 4/5) = (1/5)/(9/5) = 1/9.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 17: If tan θ = 12/5, then (1 + sin θ)/(1 − sin θ) equals
(a) 5
(b) 25
(c) 17/7
(d) 169/25
Show Answer & Explanation

Answer: (b) 25

Explanation:
1. tan θ = 12/5 gives sin θ = 12/13. So (1 + 12/13)/(1 − 12/13) = (25/13)/(1/13) = 25.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 18: If 4 tan θ = 3, then (4 sin θ − 2 cos θ)/(4 sin θ + 3 cos θ) equals
(a) 1/6
(b) 1/3
(c) 3/5
(d) 5/6
Show Answer & Explanation

Answer: (a) 1/6

Explanation:
1. tan θ = 3/4. Divide by cos θ: (4 tan θ − 2)/(4 tan θ + 3) = (3 − 2)/(3 + 3) = 1/6.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 19: If tan A = 1/2 and tan B = 1/3, then A + B equals
(a) 30°
(b) 60°
(c) 45°
(d) 90°
Show Answer & Explanation

Answer: (c) 45°

Explanation:
1. tan(A + B) = (1/2 + 1/3)/(1 − 1/6) = (5/6)/(5/6) = 1, so A + B = 45°.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

Question 20: 3π/5 radians expressed in degrees is
(a) 72°
(b) 120°
(c) 54°
(d) 108°
Show Answer & Explanation

Answer: (d) 108°

Explanation:
1. 3π/5 × 180°/π = 108°.

Teacher's Note:
1. Use the standard identities and complementary-angle relations, and substitute values carefully.
2. Check your result by testing with a simple angle where possible.

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Practice MCQs for Class 10 Mathematics Chapter 08 Introduction to Trigonometry

Download Multiple Choice Questions: Chapter 08 Introduction to Trigonometry (Class 10 Mathematics)

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Concept Clarification for Chapter 08 Introduction to Trigonometry

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FAQs

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