Q101 / 180 · COMEDK 2019 · Mathematics

The general solution of $|\sin x|=\cos x$ is (when $n \in Z$ ) given by

  • A
    $n \pi+\frac{\pi}{4}$
  • B
    $2 n \pi \pm \frac{\pi}{4}$
  • Correct answer
    C
    $n \pm \frac{\pi}{4}$
  • D
    $n \pi-\frac{\pi}{4}$

Solution

$\begin{array}{ll}\text { We have, } & |\sin x|=\cos x \\ \Rightarrow & \sin x=\pm \cos x \\ \Rightarrow & \tan x=\pm 1 \\ \Rightarrow & \tan x=\tan \left(\pm \frac{\pi}{4}\right) \\ \Rightarrow & x=n \pi \pm \frac{\pi}{4}\end{array}$

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

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