Question

The general solution of $|\sin x|=\cos x$ is (when $nϵZ)$ given by.

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

Answer 1

Answer: (B)

$2n\pi \pm \frac{\pi }{4}$

$\cos x=\left|\sin x\right|$

$\cos x=\sin x$ for $x\epsilon [0,\pi ]$

$\tan x=1$ for $x=\frac{\pi }{4}$

$\cos x=-\sin x$ for $x\epsilon [\pi ,2\pi ]$

$\tan x=-1$ for $x=\frac{7\pi }{4}$

Combining both the equations, we get

The general solution is $2n\pi \pm \frac{\pi }{4}$

Hence, B is correct.