Trigonometrical equations — ગણિત ધોરણ 11 સાયન્સ — Question

$=\tan \left(\frac{\pi}{2}-\pi \cot x\right)$

$\Rightarrow \quad \pi \tan x=\frac{\pi}{2}-\pi \cot x$

$\Rightarrow \quad \tan x+\cot x=\frac{1}{2}$

$\Rightarrow \quad \tan x+\frac{1}{\tan x}=\frac{1}{2}$

$\Rightarrow \quad 2 \tan ^{2} x+2=\tan x$

$\Rightarrow \quad 2 \tan ^{2} x-\tan x+2=0$

This is quadratic in $\tan \mathrm{x}$.

$\Rightarrow \quad \tan x=\frac{1 \pm \sqrt{1-4.4}}{4}=\frac{1 \pm \sqrt{-15}}{2}$

which are not real 

$\therefore $ solution set $=\phi$