Trigonometric Functions — Maths STD 12 Science — Question

$\cot x+\tan x=2 \operatorname{coses} x$
$\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x}=\frac{2}{\sin x}$
$\frac{\cos ^2 x+\sin ^2 x}{\sin x \cdot \cos x}=\frac{2}{\sin x}$
$\left.\frac{1}{\sin x \cdot \cos x}=\frac{2}{\sin x} \ldots \ldots \ldots \ldots \ldots \ldots \ldots [\cos ^2 x+\sin ^2 x=1\right]$
$1=\frac{2}{\sin x} \times \sin x \cdot \cos x$
$1=2 \cos x$
$\cos x=\frac{1}{2}$
$x=\cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}$
Since, $\cos \theta=\cos \alpha$ implies $\theta=2 n \pi \pm \alpha, n \in Z$
the required general solution is $x=2 n \pi \pm \frac{\pi}{3}$ where $n \in Z$