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CBSE BOARD PYQS · CHAPTER 08
Introduction to Trigonometry
CBSE Most Repeated PYQs
Solve official CBSE Previous Year Board Questions (2015-2024) for Introduction to Trigonometry. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.
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The value of (sin 30° + cos 60°) is:
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9 sec² A - 9 tan² A is equal to:
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If 15 cot A = 8, then sin A is:
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Assertion (A): The value of sin θ increases as θ increases from 0° to 90°. Reason (R): sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.
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Assertion (A): sin² A + cos² A = 1 for all 0° ≤ A ≤ 90°. Reason (R): 1 + tan² A = sec² A for all 0° ≤ A < 90°.
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If tan (A + B) = √3 and tan (A - B) = 1/√3 (0° < A + B ≤ 90°; A > B), find A and B.
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Evaluate: 2 tan² 45° + cos² 30° - sin² 60°.
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If sin (A - B) = 1/2 and cos (A + B) = 1/2, find A and B.
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Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
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Prove that (sec A + tan A)(1 - sin A) = cos A.
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Prove identity: (cosec θ - cot θ)² = (1 - cos θ) / (1 + cos θ).
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Prove identity: cos A / (1 + sin A) + (1 + sin A) / cos A = 2 sec A.
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Prove identity: tan θ / (1 - cot θ) + cot θ / (1 - tan θ) = 1 + sec θ cosec θ.
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If sin θ + cos θ = √3, prove that tan θ + cot θ = 1.
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Case Study Scenario: A surveyor measures a right triangle field ABC right angled at B. Given AB = 5 cm and ACB = 30°. Question: Find lengths of sides BC and AC.
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Case Study Scenario: In △PQR right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Question: Determine values of sin P, cos P and tan P.
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Prove: (sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A.
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Prove: (cosec A - sin A)(sec A - cos A) = 1 / (tan A + cot A).
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