Q1. [1] § 8.3 Trigonometric Ratios of Some Specific Angles § 8.5 Summary
Directions: In Question 19 and 20, Assertion (A) and Reason (R) are given. Select the correct option.
**Assertion (A):** If $\sin A = \frac{1}{3}$ $(0° < A < 90°)$, then the value of $\cos A$ is $\frac{2\sqrt{2}}{3}$.
**Reason (R):** For every angle $\theta$, $\sin^2\theta + \cos^2\theta = 1$.
- (A) Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
- (B) Both Assertion (A) and Reason (R) are true. Reason (R) does not give correct explanation of (A).
- (C) Assertion (A) is true but Reason (R) is not true.
- (D) Assertion (A) is not true but Reason (R) is true.
Previously asked in CBSE board exam
2024 30/2/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
(A) Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
Using R: $\sin^2 A + \cos^2 A = 1 \Rightarrow \cos^2 A = 1 - \frac{1}{9} = \frac{8}{9} \Rightarrow \cos A = \frac{2\sqrt{2}}{3}$, which confirms A.
Explanation
- The Reason states the Pythagorean identity $\sin^2\theta + \cos^2\theta = 1$, which is always true.
- The Assertion is verified directly by substituting $\sin A = \frac{1}{3}$ into this identity, so R directly explains A — choose option (A), not (B).
- Key tip: if R is the method used to prove A, it IS the correct explanation.
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