Question

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

• A. $\sin x-x+c$
• B. $\cos x+x+c$
• C. $\tan x-x+c$
• D. $\sec x+x+c$

Answer 1

The correct option is C $\tan x-x+c$

$\int \frac{{\sec }^{2}x}{{\text{cosec}}^{2}x}dx=\int {\tan }^{2}xdx=\int ({\sec }^{2}x-1)dx=\tan x-x+c$