Question

Evaluate : $\int \frac{1}{{\sin }^{2}x{\cos }^{2}x}dx$

• A. $(\tan x-\cot x+C)$
• B. $(\tan x+\cot x+C)$
• C. $(\tan x+2\cot x+C)$
• D. $(\tan x+3\cot x+C)$

Answer 1

The correct option is A $(\tan x-\cot x+C)$

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