JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int_0^{\frac{\pi }{2}} {\frac{{\cot \,x}}{{\cot \,x + \cos ec\,x}}} dx = m\left( {\pi + n} \right)\), then \(m.n\) is equal to
- A \(1\)
- B \(\frac{1}{2}\)
- C \(-\frac{1}{2}\)
- D \(-1\)
Answer & Solution
Correct Answer
(D) \(-1\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{\pi / 2} \frac{\cot x d x}{\cot x+\csc x}\) \(\int_{0}^{\pi / 2} \frac{\cos x}{\cos x+1}=\int \frac{2 \cos ^{2} \frac{x}{2}-1}{2 \cos ^{2} \frac{x}{2}}\) \(\int_{0}^{\pi / 2}\left(1-\frac{1}{2} \sec ^{2} \frac{x}{2}\right) d x\)…
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