Directions: Select the correct answer from the codes (A), (B), (C) and (D). Assertion (A): $\tan 2\theta$ is not defined at $\theta = 45°$. Reason (R): $\sin 90° \neq \cos 90°$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
$\tan 2\theta$ at $\theta = 45°$ means $\tan 90°$, which is not defined (since $\cos 90° = 0$). However, Reason (R) is false because $\sin 90° = 1$ and $\cos 90° = 0$, so the statement "$\sin 90° \neq \cos 90°$" is actually true — but it is not the correct reason why $\tan 90°$ is undefined. The correct reason is that $\cos 90° = 0$, making $\tan 90° = \frac{\sin 90°}{\cos 90°}$ undefined.
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Explanation
- Assertion check: $2\theta = 2 \times 45° = 90°$; $\tan 90°$ is not defined because $\cos 90° = 0$. So A is true.
- Reason check: $\sin 90° = 1 \neq 0 = \cos 90°$, so the statement "$\sin 90° \neq \cos 90°$" is mathematically true. Hence R is true.
- But R does not correctly explain A. The assertion is true because $\cos 90° = 0$ (denominator zero), not merely because $\sin 90° \neq \cos 90°$.
- Wait — re-examining: since R is actually a true statement, the answer should be (B) — both true but R is not the correct explanation.
> Correction: The answer is (B). Both A and R are true, but R is not the correct explanation of A. $\tan 90°$ is undefined because $\cos 90° = 0$, not simply because $\sin 90° \neq \cos 90°$.