Mathematics | MHT CET 2018 | Discussion Page

$\int \frac{1}{\sin x.\cos^{2}x}dx$ =

$\sec x+log |\sec x+\tan x|+C$

$\sec x\tan x+C$

$\sec x+log |\sec x-\tan x|+C$

$\sec x+log |cosec x-\cot x|+C$

Option D

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= $\sec x+log |cosec x-\cot x|+C$

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