Q107 / 180 · KCET 2012 · Mathematics

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

  • A
    $\frac{\mathrm{n} \pi}{2} \pm \frac{\pi}{4}, \mathrm{n} \in \mathrm{Z}$
  • B
    no value
  • C
    $n \pi+(-1)^{n} \frac{\pi}{4}, n \in Z$
  • Correct answer
    D
    $2 \mathrm{n} \pi \pm \frac{\pi}{2}, \mathrm{n} \in \mathrm{Z}$

Solution

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 . $\therefore \quad \cos \mathrm{x}=0$ $\Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2}$

Hence, the correct answer is option: 'D'.

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