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Class 10 Introduction to Trigonometry: 8 practice questions with answers, step by step

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These are 8 practice questions on NCERT Class 10 Maths Chapter 8, Introduction to Trigonometry, each with a worked answer and the textbook page it comes from. They cover finding the other ratios from one, using the values table, the identities, and a "prove that" question of the kind the chapter ends with. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us. The ideas behind each step are in our guide to NCERT Class 10 Chapter 8, Introduction to Trigonometry.

What the chapter says you need

Facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 8, printed pages 113 to 132):

Finding other ratios

Question 1. If sin A = 3/5 and A is acute, find cos A. (As a fraction.)

Answer: 4/5. Use sin²A + cos²A = 1: cos²A = 1 − 9/25 = 16/25, so cos A = 4/5 (positive, because A is acute).

Question 2. If sin A = 3/5 and A is acute, find tan A. (As a fraction.)

Answer: 3/4. Take a right triangle with opposite side 3 and hypotenuse 5. The adjacent side is √(5² − 3²) = √16 = 4, so tan A = opposite ÷ adjacent = 3/4. (The same method as Example 1, page 118.)

Question 3. If cos θ = 12/13 and θ is acute, find sin θ and tan θ.

Answer: sin θ = 5/13 and tan θ = 5/12. sin²θ = 1 − (12/13)² = 1 − 144/169 = 25/169, so sin θ = 5/13. Then tan θ = sin θ ÷ cos θ = (5/13) ÷ (12/13) = 5/12. Check with a right triangle: sides 5, 12, 13 and 5² + 12² = 169.

The values table

Question 4. Find sin 60° × cos 30°. (As a fraction.)

Answer: 3/4. From the table, sin 60° = √3/2 and cos 30° = √3/2, so the product is (√3/2) × (√3/2) = 3/4. (Table 8.1, page 125.)

Question 5. Find the value of sin² 30° + cos² 30°.

Answer: 1. sin 30° = 1/2 and cos 30° = √3/2, so 1/4 + 3/4 = 1. This agrees with the identity sin²A + cos²A = 1 for every angle. (Table 8.1, page 125; identity, page 128.)

Question 6. Find tan 45° + sin 90°.

Answer: 2. tan 45° = 1 and sin 90° = 1, so the sum is 2. (Table 8.1, page 125.)

Question 7. If tan A = 1 and A is acute, what is A in degrees?

Answer: 45°. From the table, tan 45° = 1, so A = 45°. (Table 8.1, page 125.)

A "prove that" question

Question 8. Prove that (1 − cos²A)(1 + cot²A) = 1.

Answer: Use two identities. sin²A + cos²A = 1 gives 1 − cos²A = sin²A (page 128). 1 + cot²A = cosec²A (page 129). So the left side is sin²A × cosec²A. Since cosec A = 1/sin A, sin²A × cosec²A = sin²A × (1/sin²A) = 1, which is the right side. (Check with A = 30°: 1 − 3/4 = 1/4 and 1 + (√3)² = 4, and 1/4 × 4 = 1.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.

The definitions, the table and the identities are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.