Question

Solve $\int \frac{dx}{\tan x+\cot x}=$

Answer 1

$\int \frac{dx}{\tan x+\cot x}$

$=\int \frac{dx}{\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}}$

$=\int \frac{\sin x\cos x}{{\sin }^{2}x+{\cos }^{2}x}$

$=\int \sin x\cos xdx$

$=\int \frac{2}{2}\sin x\cos xdx=\frac{1}{2}\int \sin 2xdx$

$=-\frac{1}{4}\cos 2x+c$