Question

General solution for $|\sin x|=\cos x$ is-

• A. $2n\pi +\frac{\pi }{4},nϵI$
• B. $2n\pi \pm \frac{\pi }{4},nϵI$
• C. $n\pi \pm \frac{\pi }{4},nϵI$
• D. None of these

Answer 1

Answer: (C)

$n\pi \pm \frac{\pi }{4},nϵI$

Consider the given expression.

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

When $\sin x<0$,

$-\sin x=\cos x$

$\tan x=-1$

$x=n\pi -\frac{\pi }{4}$

When $\sin x>0$,

$\sin x=\cos x$

$\tan x=1$

$x=n\pi +\frac{\pi }{4}$

Therefore, required set of values are,

$x=n\pi \pm \frac{\pi }{4};n\in I$

Hence, this is the required result.