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Mathematics — CBSE Class 10 board question

Q1. [1]
A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Statement A (Assertion): For $0 < \theta \leq 90°$, $\csc\theta - \cot\theta$ and $\csc\theta + \cot\theta$ are reciprocal of each other. Statement R (Reason): $\csc^2\theta - \cot^2\theta = 1$
  1. A Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).
  2. B Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).
  3. C Assertion (A) is true but Reason (R) is false.
  4. D Assertion (A) is false but Reason (R) is true.
Previously asked in CBSE board exam
2023 30/6/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:27 · grounding rag
Model Answer

Option A

Since $\csc^2\theta - \cot^2\theta = 1$, we get $(\csc\theta - \cot\theta)(\csc\theta + \cot\theta) = 1$, so the two expressions are indeed reciprocals of each other. Both A and R are true, and R directly explains A.

Explanation

The identity $\csc^2\theta - \cot^2\theta = 1$ (from the source, §8.4) can be factorised as a difference of squares to give $(\csc\theta - \cot\theta)(\csc\theta + \cot\theta) = 1$, which is precisely what "reciprocal of each other" means. So R is the correct and complete explanation of A — choose Option A.

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