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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 8.3 Trigonometric Ratios of Some Specific Angles § 8.4 Trigonometric Identities
Which of the following statements is true ?
  1. (a) $\sin 20° > \sin 70°$
  2. (b) $\sin 20° > \cos 20°$
  3. (c) $\cos 20° > \cos 70°$
  4. (d) $\tan 20° > \tan 70°$
Previously asked in CBSE board exam
2025 30/4/1 Q9
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

(c) $\cos 20° > \cos 70°$

As the angle increases from 0° to 90°, cosine decreases. So $\cos 20° > \cos 70°$. (sin and tan increase, making options a, b, d false.)

Explanation

Key rule: sin and tan are increasing functions on (0°, 90°), while cos is a decreasing function. So a smaller angle gives a larger cosine value — hence $\cos 20° > \cos 70°$ is the only true statement. Eliminate the others: sin 20° < sin 70° (sin increases), cos 20° > sin 20° only when angle < 45° but that's not what option (b) says — sin 20° < cos 20°, and tan 20° < tan 70° (tan increases). Examiners expect you to recall increasing/decreasing behaviour of trig ratios.

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