Question

If $\tan (\cot x)=\cot (\tan x)$ , then $\sin 2x$ is equal to

• A. $\frac{2}{(2n+1)\pi }$
• B. $\frac{4}{(2n+1)\pi }$
• C. $\frac{2}{n(n+1)\pi }$
• D. $\frac{4}{n(n+1)\pi }$

Answer 1

Answer: (B)

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