AP EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{\sin \left(x-\frac{\pi}{3}\right) \cos x}=\)
- A \(2 \log \left(\frac{\tan x-\sqrt{3}}{2}\right)+C\)
- B \(2 \log \left(\sin \left(x-\frac{\pi}{3}\right) \cos x\right)+C\)
- C \(2 \log (\tan x+\sqrt{3})+C\)
- D \(2 \log (\sin x+\sqrt{3} \cos x)+C\)
Answer & Solution
Correct Answer
(A) \(2 \log \left(\frac{\tan x-\sqrt{3}}{2}\right)+C\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{d x}{\sin \left(x-\frac{\pi}{3}\right) \cos x}\) \(=\int \frac{1}{\left(\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x\right) \cos x} d x\)…
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