Question

Evaluate the following
$\int \frac{1-\cot x}{1+\cot x}dx$

Answer 1

$\int \frac{1-cotx}{1+cotx}=\int \frac{sinx-cosx}{sin+cosx}$

Let, $(sinx+\cos x)=t$

$cosx-sinx=\frac{dt}{dx}$

$-\int \frac{1}{t}dt=-\ln t+C$

$=-\ln (|sinx+cosx|)+C$