COMEDK · Maths · 3. Complex Number
If \(a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+i \sin 2 \beta\), then \(\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}=\)
- A \(2 i \sin (\alpha-\beta)\)
- B 2 isin \((\alpha+\beta)\)
- C \(2 \cos (\alpha+\beta)\)
- D \(2 \cos (\alpha-\beta)\)
Answer & Solution
Correct Answer
(D) \(2 \cos (\alpha-\beta)\)
Step-by-step Solution
Detailed explanation
We have, \(a=\cos 2 \alpha+i \sin 2 \alpha\) and \(b=\cos 2 \beta+i \sin 2 \beta\) \(\frac{a}{b}=\frac{\operatorname{Cis} 2 \alpha}{\operatorname{Cis} 2 \beta}=\operatorname{Cis}(2 \alpha-2 \beta)\) So,…
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