WBJEE · Maths · Complex Number
\(1+{ }^{n} C_{1} \cos \theta+{ }^{n} C_{2} \cos 2 \theta+\ldots+{ }^{n} C_{n} \cos n \theta\) equals
- A \(\left(2 \cos \frac{\theta}{2}\right)^{n} \cos \frac{n \theta}{2}\)
- B \(2 \cos ^{2} \frac{n \theta}{2}\)
- C \(2 \cos ^{2 n} \frac{\theta}{2}\)
- D \(\left(2 \cos ^{2} \frac{\theta}{2}\right)^{n}\)
Answer & Solution
Correct Answer
(A) \(\left(2 \cos \frac{\theta}{2}\right)^{n} \cos \frac{n \theta}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(1+{ }^{n} C_{1} \cos \theta+{ }^{n} C_{2} \cos 2 \theta+\ldots+{ }^{n} C_{n} \cos n \theta\) Which is real part of complex number. \(\left({ }^{n} C_{0}+{ }^{n} C_{1} e^{i\theta}+\ldots\right)\) ie.…
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