Question

If $\cos x-\sin x\ge 1$ and $0\le x\le 2\pi$ then the solution set for $x$ is :

• A. $[0,\frac{\pi }{4}]\cup [\frac{7\pi }{4},2\pi ]$
• B. [$\frac{3\pi }{2},\frac{7\pi }{4}$], $\cup$ {0}
• C. [$\frac{3\pi }{2},2\pi$], $\cup$ {0}
• D. None of these

Answer 1

The correct option is C [$\frac{3\pi }{2},2\pi$], $\cup$ {0}

Given: $\cos x-\sin x\ge 1$ and $0\le x<2x$

To find the solution set for $x$.

The graph of $1+sinx$ is the sine graph above $y=1$ line.

According to equation,

The shaded portion is the required region and intends from $x\in [\frac{3\pi }{2},2\pi ]$

Hence the solution set of $x\in [\frac{3\pi }{2},2\pi ],\cup \left\{0\right\}$

$\therefore$ The correct option is (c) [$\frac{3\pi }{2},2\pi$], $\cup$ {0}