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

Q1. [1] § 8.2 Trigonometric Ratios § 8.3 Trigonometric Ratios of Some Specific Angles § 8.5 Summary
If $\theta$ is an acute angle of a right angled triangle, then which of the following equation is not true?
  1. A $\sin\theta \cot\theta = \cos\theta$
  2. B $\cos\theta \tan\theta = \sin\theta$
  3. C $\csc^2\theta - \cot^2\theta = 1$
  4. D $\tan^2\theta - \sec^2\theta = 1$
Previously asked in CBSE board exam
2023 30/6/1 Q16
Generated by claude-sonnet-4-6 · 2026-06-15 10:27 · grounding rag
Model Answer

Option D is not true.

The correct identity is $\sec^2\theta - \tan^2\theta = 1$, so $\tan^2\theta - \sec^2\theta = -1$, not 1.

Source: Chapter 8, Section 8.5 Summary

Explanation

The three Pythagorean identities are: $\sin^2A + \cos^2A = 1$; $\sec^2A - \tan^2A = 1$; $\cosec^2A - \cot^2A = 1$. Option D reverses the correct identity, making it wrong. Options A, B, C can be verified using basic ratio definitions and are all true.

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