Question

Find the integral of $\int \frac{{\sec }^{2}x}{co{\sec }^{2}x}dx$

Answer 1

$\int \frac{{\sec }^{2}x}{co{\sec }^{2}x}dx$
$=\int \frac{\frac{1}{{\cos }^{2}x}}{\frac{1}{{\sin }^{2}x}}dx$
$=\int \frac{{\sin }^{2}x}{{\cos }^{2}x}dx$
$=\int {\tan }^{2}xdx$
$=\int ({\sec }^{2}x-1)dx$
$=\int {\sec }^{2}xdx-\int 1dx$
$=\tan x-x+C$