Question

Anybody know the right answer

Answer 1

`\text{The domain}\\D:x\in\left(0,\ (\pi)/(2)\right)\ \cup\ \left((\pi)/(2),\ \pi\right)\\\\3\tan^2x-2=\csc^2x-\cot^2x\\\\3\tan^2x-2=(1)/(\sin^2x)-(\cos^2x)/(\sin^2x)\\\\3\tan^2x-2=(1-\cos^2x)/(\sin^2x)\\\\3\tan^2x-2=(\sin^2x)/(\sin^2x)\\\\3\tan^2x-2=1\ \ \ \ |+2\\\\3\tan^2x=3\ \ \ \ |:3\\\\\tan^2x=1\Rightarrow\tan x=\pm\sqrt1\\\\\tan x=-1\ \vee\ \tan x=1\\\\x=(3\pi)/(4)\ \vee\ x=(\pi)/(4)`

`\text{Used:}\\\\\csc x=(1)/(\sin x)\\\\\cot x=(\cos x)/(\sin x)`