TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=A \sin 2 x+B\), then \(A\) is equal to
- A \(-\frac{1}{2}\)
- B -1
- C \(\frac{1}{2}\)
- D 1
Answer & Solution
Correct Answer
(A) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x \\ & =\int \frac{\left(\sin ^4 x+\cos ^4 x\right) /\left(\sin ^4 x-\cos ^4 x\right)}{\left(\sin ^2 x+\cos ^2 x\right)^2-2 \sin ^2 x \cos ^2 x} d x \\ & =\int\left(\sin ^2 x+\cos ^2…
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