Question

Find the number of solutions of the equations;

$2^{\cos x}=\left|\sin x\right|$ when $xϵ[-2\pi ,2\pi ]$

Answer 1

We have $2^{\cos \alpha }=\left|\sin x\right|$

It is true only for $\left|\sin x\right|=1\Rightarrow \sin x=\pm 1$

$\Rightarrow x=2n\pi \pm \frac{\pi }{2}$

$\because x\in [-2\pi ,2\pi ]$

$\therefore x=-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2},-\frac{3\pi }{2}$