InterviewSolution
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InterviewSolution
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If a = cos θ + i sin θ, then \(\frac{1+a}{1-a}\) =A. cot \(\frac{θ}{2}\)B. cot θC. i cot \(\frac{θ}{2}\)D. i tan \(\frac{θ}{2}\) |
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Answer» \(\frac{1+a}{1-a}\) = \(\frac{1+(cosθ + isinθ)}{1-(cosθ + isinθ)}\) = \(\frac{1+(cosθ + isinθ)}{1-(cosθ - isinθ)}\times \frac{(1-(cosθ )+ isinθ}{(1-cosθ )+ isinθ}\) = \(\frac{2isinθ}{2-2cosθ}\) = 0 + \(i\frac{sinθ}{1-cosθ}\) = \(icot\frac{θ}{2}\) |
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