Search any question & find its solution
Question:
Answered & Verified by Expert
If $\tan (\cot x)=\cot (\tan x)$, then $\sin 2 x$ is equal to:
Options:
Solution:
2620 Upvotes
Verified Answer
The correct answer is:
$\frac{4}{(2 n+1) \pi}$
Given, $\tan (\cot x)=\cot (\tan x)=\tan \left(\frac{\pi}{2}-\tan x\right)$
$\Rightarrow \cot x=n \pi+\frac{\pi}{2}-\tan x$
$\Rightarrow \cot x+\tan x=n \pi+\frac{\pi}{2}$
$\Rightarrow \frac{1}{\sin x \cos x}=n \pi+\frac{\pi}{2} \Rightarrow \frac{1}{\sin 2 x}=\frac{n \pi}{2}+\frac{\pi}{4}$
$\Rightarrow \sin 2 x=\frac{1}{\frac{n \pi}{2}+\frac{\pi}{4}}=\frac{4}{(2 n+1) \pi}$
$\Rightarrow \cot x=n \pi+\frac{\pi}{2}-\tan x$
$\Rightarrow \cot x+\tan x=n \pi+\frac{\pi}{2}$
$\Rightarrow \frac{1}{\sin x \cos x}=n \pi+\frac{\pi}{2} \Rightarrow \frac{1}{\sin 2 x}=\frac{n \pi}{2}+\frac{\pi}{4}$
$\Rightarrow \sin 2 x=\frac{1}{\frac{n \pi}{2}+\frac{\pi}{4}}=\frac{4}{(2 n+1) \pi}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.