Question

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

Answer 1

According to question,

$\int \frac{cosx}{1-sinx}dx$

Let, $1-sinx=t$

$⟹-cosx.dx=dt$

$⟹-\int \frac{dt}{t}$

$⟹-lnt+C$

$⟹-ln(1-sinx)+C$