Question

The number of values of $x$ in $[0,2\pi ]$ satisfying the equation $|\cos x-\sin x|\ge \sqrt{2}$, is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

Given inequality is,

$|\sqrt{2}\cos (x+\frac{\pi }{4})|\ge \sqrt{2}$

This is possible only when

$\cos (x+\frac{\pi }{4})=\pm 1$

so there are $2$ solutions