COMEDK · Maths · 28. Indefinite Integration
\(\int \dfrac{\cos 4 x+1}{\cot x-\tan x} d x=\)
- A \(-\dfrac{1}{2} \cos 2 x+c\)
- B \(-\dfrac{1}{16} \cos 8 x+c\)
- C \(-\dfrac{1}{8} \cos 4 x+c\)
- D \(-\dfrac{1}{4} \cos 4 x+c\)
Answer & Solution
Correct Answer
(C) \(-\dfrac{1}{8} \cos 4 x+c\)
Step-by-step Solution
Detailed explanation
Let \(I = \int \dfrac{\cos 4x + 1}{\cot x - \tan x} dx\). Using the identity \(\cos 4x + 1 = 2 \cos^2 2x\), the numerator becomes \(2 \cos^2 2x\). The denominator is…
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