Question

If $\left|\tan x\right|\le 1$ and $xϵ[-\pi ,\pi ]$, then the solution set for $x$ is

• A. $[-\pi ,-\frac{3\pi }{4}]\cup [-\frac{\pi }{4},\frac{\pi }{4}]\cup [\frac{3\pi }{4},\pi ]$
• B. $[-\frac{\pi }{4},\frac{\pi }{4}]\cup [\frac{3\pi }{4},\pi ]$
• C. $[-\frac{\pi }{4},\frac{\pi }{4}]$
• D. none of these

Answer 1

Answer: (A)

$[-\pi ,-\frac{3\pi }{4}]\cup [-\frac{\pi }{4},\frac{\pi }{4}]\cup [\frac{3\pi }{4},\pi ]$

$\mid \tan x\mid \le 1$

$\Rightarrow -1\le \tan x\le 1$

Hence solution in $-\pi \le x\le \pi$ is,

$x\in [-\pi ,\frac{-3\pi }{4}]\cup [-\frac{\pi }{4},\frac{\pi }{4}]\cup [\frac{3\pi }{4},\pi ]$

Hence, option 'A' is correct.