Question

Number of values of $x(x\in [0,\pi \left]\right)$ for which the equation $2\sin x-2\cos x+\cot x=1$ holds good

Answer 1

$2\sin x-2\cos x+\cot x=1$
$\Rightarrow 2\sin x-2\cos x+\frac{1}{\tan x}=1$
$\Rightarrow 2\sin x\tan x-2\sin x-\tan x+1=0$
$\Rightarrow (2\sin x-1)(\tan x-1)=0$
$\sin x=\frac{1}{2}$ or $\tan x=1$
$x=\frac{\pi }{6},\frac{5\pi }{6}$ or $\frac{\pi }{4}$