Question

Integrate :
$\int \frac{{\sec }^{2}x}{\cos e{c}^{2}x}dx$

• A. $I=\tan x+x+C$
• B. $I=\cot x-x+C$
• C. $I=\tan x-x+C$
• D. None of these

Answer 1

The correct option is C $I=\tan x-x+C$

We have,

$I=\int \frac{{\sec }^{2}x}{{\csc }^{2}x}dx$

$I=\int {\tan }^{2}xdx$

$I=\int ({\sec }^{2}x-1)dx$

$I=\tan x-x+C$

Hence, this is the answer.