int frac{d x}{sin ^{2} x cos ^{2} x} equals | vedclass

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Question

(A) Let $I = \int \frac{d x}{\sin ^{2} x \cos ^{2} x}$.We know that $1 = \sin ^{2} x + \cos ^{2} x$.Substituting this in the integral,we get:$I = \int

Vedclass · Accepted Answer

$	an x - \cot x + C$

Vedclass · Answer

(A) Let $I = \int \frac{d x}{\sin ^{2} x \cos ^{2} x}$.We know that $1 = \sin ^{2} x + \cos ^{2} x$.Substituting this in the integral,we get:$I = \int \frac{\sin ^{2} x + \cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x$$I = \int \frac{\sin ^{2} x}{\sin ^{2} x \cos ^{2} x} d x + \int \frac{\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x$$I = \int \frac{1}{\cos ^{2} x} d x + \int \frac{1}{\sin ^{2} x} d x$$I = \int \sec ^{2} x d x + \int \csc ^{2} x d x$Using the standard integration formulas $\int \sec ^{2} x d x = 	an x + C_1$ and $\int \csc ^{2} x d x = -\cot x + C_2$:$I = 	an x - \cot x + C$.Hence,the correct option is $A$.

$\int \frac{d x}{\sin ^{2} x \cos ^{2} x}$ equals

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