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If $\sin 2 x=4 \cos x$, then $x$ is equal to
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1103 Upvotes
Verified Answer
The correct answer is:
$2 n \pi \pm \frac{\pi}{2}, n \in Z$
We have, $\sin 2 x=4 \cos x \Rightarrow 2 \sin x \cos x=4 \cos x$
$$
\begin{aligned}
&\Rightarrow \quad \cos x(\sin x-2)=0 \Rightarrow \cos x=0 \quad[\because \sin x \neq 2] \\
&\Rightarrow \quad \cos x=0=\cos \pi / 2 \Rightarrow x=2 n \pi \pm \frac{\pi}{2}, n \in \mathrm{Z}
\end{aligned}
$$
$$
\begin{aligned}
&\Rightarrow \quad \cos x(\sin x-2)=0 \Rightarrow \cos x=0 \quad[\because \sin x \neq 2] \\
&\Rightarrow \quad \cos x=0=\cos \pi / 2 \Rightarrow x=2 n \pi \pm \frac{\pi}{2}, n \in \mathrm{Z}
\end{aligned}
$$
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