MCQ
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
- A$(2n + 1)\frac{\pi }{4}$
- ✓$\frac{4}{{(2n + 1)\pi }}$
- C$4\pi (2n + 1)$
- DNone of these
$ \Rightarrow $ $\tan (\cot x) = \tan \left( {\frac{\pi }{2} - \tan x} \right)$
$ \Rightarrow $ $\cot x = n\pi + \frac{\pi }{2} - \tan x $
$\Rightarrow \cot x + \tan x = n\pi + \frac{\pi }{2}$
$ \Rightarrow $ $\frac{2}{{\sin 2x}} = n\pi + \frac{\pi }{2}$
$\Rightarrow \sin 2x = \frac{2}{{n\pi + \frac{\pi }{2}}} = \frac{4}{{(2n + 1)\pi }}$
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