^2x.cosec^2xdx= 1. - +c 2. + +c 3. - + +c 4. +c - Vidyadip

Question

$\int\sec^2\text{x}.\text{cosec}^2\text{xdx}=$

$\tan\text{x}-\cot\text{x+c}$
$\tan\text{x}+\cot\text{x+c}$
$-\tan\text{x}+\cot\text{x+c}$
$\sec\text{x}\tan\text{x+c}$

✓

Answer

$\tan\text{x}-\cot\text{x+c}$

Solution:
$\int\sec^2\text{x}.\text{cosec}^2\text{xdx}$
$=\int\frac{{1}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$
$=\int\frac{{{{\cos^2\text{x.}\sin^2\text{x}}}}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$
$=\int\frac{{{{\cos^2\text{x.}}}}}{{\cos^2\text{x}\sin^2\text{x}}}+\frac{{{{\sin^2\text{x}}}}}{{\cos^2\text{x.}\sin^2\text{x}}}\text{dx}$
$=\int(\text{cosec}^2\text{x}+\sec^2\text{x})\text{dx}$
$=-\cot\text{x}+\tan\text{x}+\text{c}$
$=\tan\text{x}-\cot\text{x+c}$

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