Evaluate: `int1/(sin^2x cos^2x)\ dx`

Explanation

Solution:

` \frac{1}{\sin ^{2} x \cdot \cos ^{2} x} d x Rightarrow \sin ^{2} x \cdot \cos ^{2} x \sin 2 x`

=`2 \sin x \cdot \cos x`

=`(\sin x \cdot \cos x)^{2} \frac{1}{2} \sin 2 x=\sin x \cdot \cos x`

=`(\frac{1}{2} \sin 2 x)^{2}`

=` \frac{1}{4} \sin ^{2} 2 x `

= `\int \frac{1}{\frac{1}{4} \sin ^{2} 2 x} d x `

=` \int(\frac{1}{4} \sin ^{2} 2 x)^{-1} d x`

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