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Class 10 › Mathematics › Introduction to Trigonometry
CBSE2026Class Class 10 · Mathematics1 Marks · Long✅ Verified
Assertion (A) : $\tan 2\theta$ is not defined at $\theta = 45^\circ$.
Reason (R) : $\sin 90^\circ \neq \cos 90^\circ$.
✅ Answer & Solution
Step 1: Check Assertion (A). At $\theta = 45^\circ$, $2\theta = 90^\circ$ and
$$\tan 90^\circ = \frac{\sin 90^\circ}{\cos 90^\circ} = \frac{1}{0}$$
which is not defined. So Assertion (A) is TRUE.
Step 2: Check Reason (R). $\sin 90^\circ = 1$ and $\cos 90^\circ = 0$, so $\sin 90^\circ \neq \cos 90^\circ$. Reason (R) is TRUE.
Step 3: However, $\tan 90^\circ$ is undefined because $\cos 90^\circ = 0$ (denominator zero), not merely because the two ratios are unequal. So R is NOT the correct explanation of A.
