If 4 sin

Question:

If $4 \sin ^{2} x=1$, then the values of $x$ are

(a) $2 n \pi \pm \frac{\pi}{3}, n \in Z$

(b) $n \pi \pm \frac{\pi}{3}, n \in Z$

(c) $n \pi \pm \frac{\pi}{6}, n \in Z$

(d) $2 n \pi \pm \frac{\pi}{6}, n \in Z$

Solution:

(c) $n \pi \pm \frac{\pi}{6}, n \in Z$

Given;

$4 \sin ^{2} x=1$

$\Rightarrow \sin ^{2} x=\frac{1}{4}$

$\Rightarrow \sin x=\frac{1}{2} \quad$ or $\quad \sin x=-\frac{1}{2}$

$\Rightarrow \sin x=\sin \frac{\pi}{6} \quad$ or $\sin x=\sin \left(-\frac{\pi}{6}\right)$

$\Rightarrow x=n \pi+(-1)^{n} \frac{\pi}{6}, n \in Z \quad$ or $x=n \pi+(-1)^{n}\left(-\frac{\pi}{6}\right), n \in Z$

$\Rightarrow x=n \pi \pm \frac{\pi}{6}, n \in Z$

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