Question

The number of solutions of the equation $\sqrt{1-\sin x}=\cos x$ in the interval $[0,3\pi ]$ is

• A. $2$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

$\sqrt{1-\sin x}=\cos x\cdots \left(1\right)$
$\Rightarrow 1-\sin x={\cos }^{2}x$
$\Rightarrow \sin x(\sin x-1)=0$
$\Rightarrow \sin x=0\text{or}\sin x=1$
$\Rightarrow x=0,\pi ,2\pi ,3\pi \text{or}x=\frac{\pi }{2},\frac{5\pi }{2}$

But $x=\pi ,3\pi$ do not satisfy equation $\left(1\right).$
$\therefore$ Total number of solutions is $4.$