Question

Find the value of $\int \frac{{\sec }^{2}x}{cose{c}^{2}dx}dx$

Answer 1

$\int \frac{{\sec }^{2}x}{{\csc }^{2}x}dx=\int \frac{1/{\cos }^{2}x}{1/{\sin }^{2}x}dx=\int {\tan }^{2}x$

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

Use basic formulas