Question

Evaluate : $\int \frac{{\sec }^{2}x}{{\text{cosec}}^{2}x}dx$

Answer 1

Let $I=\int \frac{se{c}^{2}x}{cose{c}^{2}x}dx$

We know that, $\csc x=\frac{1}{\sin x}$ and $\sec x=\frac{1}{\cos x}$

$I=\int ta{n}^{2}xdx$

$=\int (se{c}^{2}x-1)dx$

$I=tanx-x+C$