AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{1+\cos (4 x)}{\cot (x)-\tan (x)} d x=k \cos (4 x)+c\), then
- A \(k=\frac{1}{8}\)
- B \(k=\frac{1}{4}\)
- C \(k=\frac{-1}{8}\)
- D \(k=\frac{-1}{4}\)
Answer & Solution
Correct Answer
(C) \(k=\frac{-1}{8}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} I & =\int \frac{1+\cos 4 x}{\cot x-\tan x} d x \\ & =\int \frac{2 \cos ^2(2 x)}{\frac{\cos ^2 x-\sin ^2 x}{\sin x \cdot \cos x}} d x=\int 2 \cos 2 x \sin x \cos x d x \\ & =\frac{1}{2} \int \sin 4 x d x=\frac{-1}{8} \cos (4 x)+c=k \cos (4 x)+c \quad…
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