Mathematics - Trigonometric Equation Question with Solution | TestHub

Given, $\tan (\cot x)=\cot (\tan x)=\tan \left(\frac{\pi }{2}-\tan x\right)$ $\Rightarrow \cot x=n\pi +\frac{\pi }{2}-\tan x$ $\Rightarrow \cot x+\tan x=n\pi +\frac{\pi }{2}$ $\Rightarrow \frac{1}{\sin x\cos x}=n\pi +\frac{\pi }{2}\Rightarrow \frac{1}{\sin 2x}=\frac{n\pi }{2}+\frac{\pi }{4}$ $\Rightarrow \sin 2x=\frac{1}{\frac{n\pi }{2}+\frac{\pi }{4}}=\frac{4}{(2n+1)\pi }$