Question

Find the number of solutions of $2\cos x=\left|\sin x\right|$ when $x\in [0,4\pi ]$

Answer 1

$2cos\left(x\right)=|sin\left(x\right)|$
Case $I$
$2cos\left(x\right)=-sin\left(x\right)$
$tan\left(x\right)=-2$
$x=ta{n}^{-1}(-2)$. Hence there will be two values of x, one in second quadrant and another in 4th quadrant.
Case $II$
$2cos\left(x\right)=sin\left(x\right)$
$tan\left(x\right)=2$
$x=ta{n}^{-1}\left(2\right)$. Hence there will be two values of x, one in 1st quadrant and another in 3th quadrant.
Hence there will be 4 solution to the above equation.