📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
Home › Mathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
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.

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.