Question

Integrate the following function w.r.t $x$
$\frac{\cos x}{1-\sin x}$

Answer 1

According to question,
$\int \frac{\cos x}{1-\sin x}dx$
Let, $1-sinx=t$
$\Rightarrow$ $-cosx.dx=dt$
$\Rightarrow$ $\int -\frac{1}{t}dt$
$-lnt+C$
$\Rightarrow$ $-ln(1-sinx)+C$