Question

Solve $\tan x>\cot x$, where $x\in [0,2\pi ]$

• A. $xϵ(\pi /4,\pi /2)$
• B. $xϵ(3\pi /4,\pi )$
• C. $xϵ(5\pi /4,3\pi /2)$
• D. $xϵ(7\pi /4,2\pi )$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $xϵ(\pi /4,\pi /2)$
B $xϵ(3\pi /4,\pi )$
C $xϵ(5\pi /4,3\pi /2)$
D $xϵ(7\pi /4,2\pi )$

Given, $\tan x>\cot x$

$\frac{\sin x}{\cos x}>\frac{\cos x}{\sin x}$

${\sin }^{2}x>{\cos }^{2}x$

${\sin }^{2}x-{\cos }^{2}x>0$

$-\cos \left(2x\right)>0$

$\cos 2x<0$

$2x\in [\frac{\pi }{2},\pi ]\cup [\pi ,\frac{3\pi }{2}]$

$x\in [\frac{\pi }{4},\frac{\pi }{2}]\cup [\frac{\pi }{2},\frac{3\pi }{4}]$

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