Question

Number of solution(s) of the equation $\cos x+2\sin x=1,x\in (0,2\pi ]$ is

Answer 1

$\cos x+2\sin x=1\Rightarrow 2\sin x=1-\cos x$

We draw the graph of LHS and RHS in the range $(0,2\pi ]$

(Image )

So from the graph we have two solutions for the equation in the region $(0,2\pi ]$