Question

If $\sin ^2 \theta=\frac{1}{4}$, then the most general value of $\theta$ is

(A) $2 n \pi \pm(-1)^n \frac{\pi}{6}$

(B) $\frac{n \pi}{2} \pm(-1)^n \frac{\pi}{6}$

(C) $n \pi \pm \frac{\pi}{6}$

(D) $2 n \pi \pm \frac{\pi}{6}$

Answer 1

$\begin{aligned}\sin ^2 \theta & =\frac{1}{4} \\\sin ^2 \theta & =\sin ^2 \frac{\pi}{6} \\\theta & =n \pi \pm \frac{\pi}{6}\end{aligned}$

So, The correct option will be (C).