TS EAMCET · Maths · Definite Integration
\(\int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}=\)
- A \(0\)
- B \(\frac{1}{2} \log (2-\sqrt{3})\)
- C \(\frac{1}{2} \log (2+\sqrt{3})\)
- D \(\frac{1}{2} \log (2 \sqrt{3}-3)\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2} \log (2 \sqrt{3}-3)\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x} = \int_0^{\frac{\pi}{2}} \frac{d x}{2\left(\frac{1}{2}\cos x - \frac{\sqrt{3}}{2}\sin x\right)}\) \(= \int_0^{\frac{\pi}{2}} \frac{d x}{2\left(\cos\frac{\pi}{3}\cos x - \sin\frac{\pi}{3}\sin x\right)}\)…
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