Answer:
Option D
Explanation:
We have,
l= $\int \frac{1}{\sin x.\cos^{2}x}dx$
$\Rightarrow$ $l=\int \frac{\sin^{2}x+\cos^{2}x}{\sin x.\cos^{2}x}dx$
$\Rightarrow$ $l=\int \frac{\sin^{2}x}{\sin x.\cos^{2}x}dx+\int \frac{\cos^{2}x}{\sin x.\cos^{2}x}dx$
$\Rightarrow$ $l=\int sec x \tan xdx+\int cosec x dx$
$\Rightarrow$ l= $\sec x+log |cosec x-\cot x|+C$
