Question

Evaluate $\int \frac{dx}{si{n}^{2}Xco{s}^{2}X}$

Answer 1

$\int \frac{dx}{{\sin }^{2}x{\cos }^{2}x}=\int cose{c}^{2}x{\sec }^{2}xdx=\int (1+{\cot }^{2}x){\sec }^{2}xdx$

$=\int {\sec }^{2}xdx+\int cose{c}^{2}xdx=\tan x-\cot x+c$.