CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23

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

Explore reliable objective questions for Chapter 08 Introduction to Trigonometry tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Practice Chapter 08 Introduction to Trigonometry MCQs for Class 10 Mathematics

Access the complete set of multiple-choice questions for Chapter 08 Introduction to Trigonometry below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: 150° expressed in radians is
(a) 3π/4
(b) 5π/6
(c) 2π/3
(d) 7π/6
Show Answer & Explanation

Answer: (b) 5π/6

Explanation:
1. 150 × π/180 = 5π/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 2: If tan θ = x/y, then (x sin θ + y cos θ)/(x sin θ − y cos θ) equals
(a) (x + y)/(x − y)
(b) (x² − y²)/(x² + y²)
(c) (x² + y²)/(x² − y²)
(d) x/y
Show Answer & Explanation

Answer: (c) (x² + y²)/(x² − y²)

Explanation:
1. Divide numerator and denominator by cos θ: (x tan θ + y)/(x tan θ − y) = (x²/y + y)/(x²/y − y) = (x² + y²)/(x² − y²).

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: If 5 tan θ = 4, then (5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ) equals
(a) 1/7
(b) 1/3
(c) 3/7
(d) 1/6
Show Answer & Explanation

Answer: (d) 1/6

Explanation:
1. tan θ = 4/5. Divide by cos θ: (5 tan θ − 3)/(5 tan θ + 2) = (4 − 3)/(4 + 2) = 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 4: If 16 cot x = 12, then (sin x − cos x)/(sin x + cos x) equals
(a) 1/7
(b) 1/3
(c) 3/7
(d) 7
Show Answer & Explanation

Answer: (a) 1/7

Explanation:
1. cot x = 3/4 so tan x = 4/3. Dividing by cos x: (tan x − 1)/(tan x + 1) = (1/3)/(7/3) = 1/7.

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 5: If 8 tan x = 15, then sin x − cos x equals
(a) 23/17
(b) 1/17
(c) 7/8
(d) 7/17
Show Answer & Explanation

Answer: (d) 7/17

Explanation:
1. tan x = 15/8 gives hypotenuse 17. sin x = 15/17 and cos x = 8/17. The difference is 7/17.

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 6: If tan θ = 1/√7, then (cosec² θ − sec² θ)/(cosec² θ + sec² θ) equals
(a) 1/4
(b) 3/5
(c) 3/4
(d) 4/3
Show Answer & Explanation

Answer: (c) 3/4

Explanation:
1. cosec² θ = 1 + cot² θ = 8 and sec² θ = 1 + tan² θ = 8/7. The ratio is (8 − 8/7)/(8 + 8/7) = (48/7)/(64/7) = 3/4.

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: If cot θ = 1/√3, then (1 − cos² θ)/(2 − sin² θ) equals
(a) 3/4
(b) 1/5
(c) 3/7
(d) 3/5
Show Answer & Explanation

Answer: (d) 3/5

Explanation:
1. cot θ = 1/√3 gives tan θ = √3 and θ = 60°. sin² 60° = 3/4, so the value is (3/4)/(2 − 3/4) = (3/4)/(5/4) = 3/5.

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: If 3 cos θ = 5 sin θ, then (5 sin θ − 2 sec³ θ + 2 cos θ)/(5 sin θ + 2 sec³ θ − 2 cos θ) equals
(a) 979/271
(b) 271/1089
(c) 271/979
(d) 3/5
Show Answer & Explanation

Answer: (c) 271/979

Explanation:
1. Divide numerator and denominator by cos θ. tan θ = 3/5, so sec² θ = 1 + 9/25 = 34/25 and sec⁴ θ = 1156/625. Numerator: 5 tan θ − 2 sec⁴ θ + 2 = 3 − 2312/625 + 2 = 813/625. Denominator: 3 + 2312/625 − 2 = 2937/625. The ratio is 813/2937 = 271/979.

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: If tan θ = 3/4, then cos² θ − sin² θ equals
(a) 1/25
(b) 7/5
(c) 7/25
(d) 24/25
Show Answer & Explanation

Answer: (c) 7/25

Explanation:
1. cos² θ = 16/25 and sin² θ = 9/25. The difference is 7/25.

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 10: The value of tan 75° is
(a) 2 − √3
(b) 2 + √3
(c) √3 + 1
(d) √3 − 1
Show Answer & Explanation

Answer: (b) 2 + √3

Explanation:
1. tan 75° = tan(45° + 30°) = (1 + 1/√3)/(1 − 1/√3) = (√3 + 1)/(√3 − 1) = (√3 + 1)²/2 = 2 + √3.

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: If 3 sin x + 5 cos x = 5, then (3 cos x − 5 sin x)² equals
(a) 9
(b) 25
(c) 16
(d) 1
Show Answer & Explanation

Answer: (a) 9

Explanation:
1. (3 sin x + 5 cos x)² + (3 cos x − 5 sin x)² = 9 + 25 = 34. So (3 cos x − 5 sin x)² = 34 − 25 = 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 12: The value of (sin A + cos A)² + (sin A − cos A)² is
(a) 2
(b) 1
(c) 0
(d) 4
Show Answer & Explanation

Answer: (a) 2

Explanation:
1. Expanding, the cross terms cancel: 2 sin² A + 2 cos² A = 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: The value of √((1 + sin A)/(1 − sin A)) is
(a) sec A + tan A
(b) sec A − tan A
(c) cosec A + cot A
(d) cos A + tan A
Show Answer & Explanation

Answer: (a) sec A + tan A

Explanation:
1. Multiply numerator and denominator by (1 + sin A): √((1 + sin A)²/cos² A) = (1 + sin A)/cos A = sec A + tan A.

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: The value of √((1 − cos x)/(1 + cos x)) is
(a) cosec x + cot x
(b) sec x − tan x
(c) sin x − cos x
(d) cosec x − cot x
Show Answer & Explanation

Answer: (d) cosec x − cot x

Explanation:
1. Multiply numerator and denominator by (1 − cos x): √((1 − cos x)²/sin² x) = (1 − cos x)/sin x = cosec x − cot x.

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: The value of √((sec x − tan x)/(sec x + tan x)) is
(a) sec x − tan x
(b) sec x + tan x
(c) cosec x − cot x
(d) cos x − sin x
Show Answer & Explanation

Answer: (a) sec x − tan x

Explanation:
1. Multiply numerator and denominator by (sec x − tan x): √((sec x − tan x)²/(sec² x − tan² x)) = sec x − tan x, since sec² x − tan² x = 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 16: The value of sin 15° is
(a) (√3 + 1)/(2√2)
(b) (√3 − 1)/2
(c) (√3 − 1)/(2√2)
(d) 1/(2√2)
Show Answer & Explanation

Answer: (c) (√3 − 1)/(2√2)

Explanation:
1. sin 15° = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° = (√3 − 1)/(2√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 17: The value of sin 40° − cos 50° is
(a) 1
(b) −1
(c) sin 10°
(d) 0
Show Answer & Explanation

Answer: (d) 0

Explanation:
1. cos 50° = sin(90° − 50°) = sin 40°, so the difference is 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 18: If x = r sin A cos B, y = r sin A sin B and z = r cos A, then
(a) x² + y² + z² = r²
(b) x² − y² + z² = r²
(c) x² + y² − z² = r²
(d) −x² + y² + z² = r²
Show Answer & Explanation

Answer: (a) x² + y² + z² = r²

Explanation:
1. x² + y² = r² sin² A (cos² B + sin² B) = r² sin² A. Adding z² = r² cos² A gives x² + y² + z² = r².

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: The value of cot 15° cot 16° cot 17° ... cot 73° cot 74° cot 75° is
(a) 1
(b) 0
(c) 2
(d) 75
Show Answer & Explanation

Answer: (a) 1

Explanation:
1. Pair the terms cot k° and cot(90° − k°); their product is 1. The middle term is cot 45° = 1. So the whole product 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.

Free study material for Mathematics

Multiple Choice Questions (MCQs) for Class 10 Mathematics Chapter 08 Introduction to Trigonometry

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

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

Concept Clarification for Chapter 08 Introduction to Trigonometry

Each question includes structured solution keys mapped directly to standard CBSE textbooks, helping students evaluate their reasoning and correct mistakes early in their revision.

Additional Study Resources for Class 10 Mathematics

Wrap up your chapter revision by testing your knowledge against standard question formats. Everything on our platform is provided free of charge.

FAQs

Where can I access latest CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23?

You can get most exhaustive CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23 for free on StudiesToday.com. These MCQs for Class 10 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in Class 10 exams?

By solving our CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23, Class 10 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23?

Yes, Mathematics MCQs for Class 10 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

Can I practice these Mathematics Class 10 MCQs online?

Yes, you can also access online interactive tests for CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 23 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.