Question

find intigration of the above

Answer 1

hope this helps you .

Answer 2

Solution:-

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

can we be written as

$\implies \int \: \frac{ \sin {}^{2} {}^{} x + \cos {}^{2}x }{ \sin {}^{2} x\cos {}^{2}x }dx \\ \\ \implies \int \: \frac{ \cancel{\sin {}^{2}x } }{ \cancel{\sin {}^{2}x } \cos {}^{2}x }d x + \int \: \frac{ \cancel{ \cos {}^{2}x} }{ \sin {}^{2} x \cancel{\cos {}^{2} x }} dx$

$\implies \int \: \frac{1}{ \cos {}^{2} x }dx + \frac{1}{ \sin {}^{2}x } dx \\ \\ \implies \int \: \sec {}^{2} x \: dx \: + \int \: \cosec \: {}^{2}x \: dx \\ \\ \implies \tan \: x - \cot \: x + c$

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option D is ✅

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I hope it helps you