If sin 2x = 4 cos x,then x is equal to | vedclass

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(D) Given,$\sin 2x = 4 \cos x$. Using the identity $\sin 2x = 2 \sin x \cos x$,we have: $2 \sin x \cos x = 4 \cos x$ $2 \sin x \cos x - 4 \cos x = 0$

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$2n \pi \pm \frac{\pi}{2}, n \in Z$

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(D) Given,$\sin 2x = 4 \cos x$. Using the identity $\sin 2x = 2 \sin x \cos x$,we have: $2 \sin x \cos x = 4 \cos x$ $2 \sin x \cos x - 4 \cos x = 0$ $2 \cos x (\sin x - 2) = 0$ This implies either $\cos x = 0$ or $\sin x = 2$. Since the range of $\sin x$ is $[-1, 1]$,$\sin x = 2$ has no real solution. Thus,$\cos x = 0$. The general solution for $\cos x = 0$ is $x = (2n + 1) \frac{\pi}{2}$,which can be written as $x = n \pi + \frac{\pi}{2}$ or $x = 2n \pi \pm \frac{\pi}{2}$ for $n \in Z$.

If $\sin 2x = 4 \cos x$,then $x$ is equal to

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