Question

Number of solutions of $2\cos X=|\sin X|$ , $0\le X\le 4\pi$ is

• A. $0$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is C $4$

$2\cos X=\left|\sin X\right|,0\le X\le 4\pi \Rightarrow 2\cos X=\sin X,0\le X\le 2\pi \Rightarrow 2\cos X=-\sin X,2\pi <X\le 4\pi \Rightarrow \tan X=2,0\le X\le 2\pi \Rightarrow \tan X=-2,2\pi <X\le 4\pi$

From the figure it is clear that there are total 4 solution for the equation given below

Correct option is C