Question

Evaluate : $\int {\left(\tan x-\cot x\right)}^{2}dx$

Answer 1

$\int {\tan }^{2}x+co{t}^{2}x-2dx$ $(a-b{)}^2=a^2+b^2-2ab$

$\int {\sec }^{2}x-1+cose{c}^{2}x-1-2dx$ $se{c}^{2}x=1+ta{n}^{2}x$

$\int {\sec }^{2}x+cose{c}^{2}x-4dx$

$\int {\sec }^{2}xdx+\int cose{c}^{2}xdx-\int 4dx$

$tanx-cotx-4x+c$