Question

Number of solution of the equation |sin x | = sin x + 2 cos x , in the interval $[0,2\pi ]$

• A. One
• B. Two
• C. Three
• D. Four

Answer 1

The correct option is B Two

$|sinx|=sinx+2\cos x$
When $\sin x>0$ or $0\ge x<\pi$
The equation is, $\sin x=\sin x+2\cos x$
$\cos x=0$
$x=\frac{\pi }{2}$
When, $\sin x<0$ or $\pi <x\le 2\pi$
The equation is, $-\sin x=\sin x+2\cos x$
$-2\sin x=2\cos x$
$\tan x=-1$
$\tan x=\tan 7pi8$
$x=\frac{7\pi }{8}$
Thus, there are two solutions.