Question:
\(\int \frac{\mathrm{d} x}{\sin ^{2} x \cos ^{2} x}\) is equal to
\(\int \frac{\mathrm{d} x}{\sin ^{2} x \cos ^{2} x}\) is equal to
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Write \(1=\sin^2 x+\cos^2 x\) in the numerator and split the fraction.
Updated On: Nov 12, 2026
- \(\tan x+\cot x+c\)
- \((\tan x+\cot x)^{2}+c\)
- \(\tan x-\cot x+c\)
- \(2(\sec x \tan x-\operatorname{cosec} x \cot x)+c\)
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The Correct Option is C
Solution and Explanation
\(\frac{1}{\sin^2 x\cos^2 x}=\frac{\sin^2 x+\cos^2 x}{\sin^2 x\cos^2 x}=\sec^2 x+\operatorname{cosec}^2 x\).
\(\int(\sec^2 x+\operatorname{cosec}^2 x)\,dx=\tan x-\cot x+c\).
Answer: (3) \(\tan x-\cot x+c\)
\(\int(\sec^2 x+\operatorname{cosec}^2 x)\,dx=\tan x-\cot x+c\).
Answer: (3) \(\tan x-\cot x+c\)
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