TS EAMCET · Maths · Definite Integration
If \(\cos x+\cos 2 x+\ldots+\cos n x=\frac{A(x)}{2 \sin x / 2}\), then \(\int_0^\pi A(x) d x=\)
- A \(\frac{n^2}{n+1}\)
- B \(\frac{-4 n}{2 n+1}\)
- C \(\frac{2 n}{2 n+1}\)
- D \(\frac{-n}{2 n+1}\)
Answer & Solution
Correct Answer
(B) \(\frac{-4 n}{2 n+1}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } \cos x+\cos 2 x+\ldots+\cos n x=\frac{A(x)}{2 \sin x / 2} \\ & \therefore \quad A(x)=2 \cos \left(x+\frac{(n-1)}{2} x\right) \sin \frac{n x}{2} \\ & A(x)=2 \cos \left(\frac{n+1}{2}\right) x \sin \frac{n x}{2} \\ & A(x)=\sin \left(\frac{2…
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