Question
यदि $\tan (\cot x) = \cot (\tan x),$ तो $\sin 2x =$
$ \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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$(S2)$ : $13(13)^n-11 \mathrm{n}-13$ अनंत $\mathrm{n} \in \mathrm{N}$ के लिए
$144$ से विभाज्य हैमें से
$A_1=\left\{(x, y): x^2+2 y^2 \leq 1\right\}$
$A_2=\left\{(x, y):\left|x^3\right|+2 \sqrt{2} \mid y^3 \leq 1\right\}$
$A_3=\{(x, y): \max (|x|, \sqrt{2}|y|) \leq 1\}$ तब