COMEDK · Maths · 28. Indefinite Integration
The value of \(\int \frac{1}{1-\cos 4 x} d x\) is
- A \(\frac{\cot 2 x+c}{2}\)
- B \(\frac{-\cot 2 x+c}{4}\)
- C \(2 \cot 2 x+c\)
- D \(\frac{-\cot 2 x+c}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{-\cot 2 x+c}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } I=\int \frac{1}{1-\cos 4 x} d x \\ & I=\int \frac{1}{2 \sin ^2 2 x} d x \quad\left[\because 1-\cos 2 \theta=2 \sin ^2 \theta\right] \\ & \quad I=\frac{1}{2} \int \operatorname{cosec}^2 2 x d x\end{aligned}\)…
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