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If $\sin 2 x=4 \cos x$, then $x$ is equal to
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Verified Answer
The correct answer is:
$2 \mathrm{n} \pi \pm \frac{\pi}{2}, \mathrm{n} \in \mathrm{Z}$
Given, $\sin 2 x=4 \cos x$
$$
\begin{aligned}
&\Rightarrow \quad 2 \sin x \cos x=4 \cos x \\
&\Rightarrow \quad 2 \cos x(\sin x-2)=0
\end{aligned}
$$
$\Rightarrow \sin x=2$, which is not possible because the value of $\sin x$ lies between $-1$ and 1 .
$\therefore \quad \cos \mathrm{x}=0$
$\Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2}$
$$
\begin{aligned}
&\Rightarrow \quad 2 \sin x \cos x=4 \cos x \\
&\Rightarrow \quad 2 \cos x(\sin x-2)=0
\end{aligned}
$$
$\Rightarrow \sin x=2$, which is not possible because the value of $\sin x$ lies between $-1$ and 1 .
$\therefore \quad \cos \mathrm{x}=0$
$\Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2}$
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