Question

The intervals for which $\tan x>\cot x$, where $x\in (0,\pi )-\left\{\frac{\pi }{2}\right\}$ is

• A. $(0,\frac{\pi }{4})\cup (\frac{3\pi }{4},\pi )$
• B. $(0,\frac{\pi }{4})\cup (\frac{\pi }{2},\frac{3\pi }{4})$
• C. $(\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{\pi }{2},\frac{3\pi }{4})$
• D. $(\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{3\pi }{4},\pi )$

Answer 1

The correct option is D $(\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{3\pi }{4},\pi )$


We need to evaluate the values of $x$ for which the graph of $y=\tan x$ is above the graph of $y=\cot x$
We know that, $\tan x=\cot x$ at $x=\frac{\pi }{4}$ in $Q_1$ and $\frac{3\pi }{4}$ in $Q_2.$

From graph,
$\tan x>\cot x\Rightarrow x\in (\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{3\pi }{4},\pi )$