Mathematics

$$\int \frac{1}{sin^{2}xcos^{2}x}dx$$


SOLUTION
$$ \int \frac{1}{sin^{2}x.cos^{2}x} dx \Rightarrow sin^{2}x.cos^{2}x$$  $$ sin\,2x = 2\,sin\,x.cos\,x$$
$$ = (sinx.cosx)^{2}$$  $$ \frac{1}{2} sin\,2x = sin\,x.cos\,x$$
$$ = (\frac{1}{2} sin\,2x)^{2}$$
$$ = \frac{1}{4} sin^{2}\,2x$$
$$ = \int \frac{1}{\frac{1}{4}sin^{2}2x}dx$$
$$ = \int (\frac{1}{4} sin^{2}2x)^{-1}dx$$     
$$ = \int 4 \,cosec^{2}\,2x.dx$$  $$ \int \,cosec^{2}\,x=-cotx\,$$
$$ = -4\,cot\,2x \times \frac{1}{2} + c $$
$$=  -2\,cot \,2x + c $$
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Subjective Medium Published on 17th 09, 2020
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