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Question: Answered & Verified by Expert
If $\sin 2 x=4 \cos x$, then $x$ is equal to
MathematicsTrigonometric EquationsCOMEDKCOMEDK 2021
Options:
  • A $\frac{n \pi}{2} \pm \frac{\pi}{4}, n \in Z$
  • B no value
  • C $n \pi+(-1)^{n} \frac{\pi}{4}, n \in Z \quad$
  • D $2 n \pi \pm \frac{\pi}{2}, n \in Z$
Solution:
1103 Upvotes Verified Answer
The correct answer is: $2 n \pi \pm \frac{\pi}{2}, n \in Z$
We have, $\sin 2 x=4 \cos x \Rightarrow 2 \sin x \cos x=4 \cos x$
$$
\begin{aligned}
&\Rightarrow \quad \cos x(\sin x-2)=0 \Rightarrow \cos x=0 \quad[\because \sin x \neq 2] \\
&\Rightarrow \quad \cos x=0=\cos \pi / 2 \Rightarrow x=2 n \pi \pm \frac{\pi}{2}, n \in \mathrm{Z}
\end{aligned}
$$

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