COMEDK · Maths · 2. Quadratic Equation
If \(x+\frac{1}{x}=2 \cos \alpha\), then \(x^{n}+\frac{1}{x^{n}}\) is equal to
- A \(2^{n} \cos \alpha\)
- B \(2^{n} \cos n \alpha\)
- C \(2 i \sin n \alpha\)
- D \(2 \cos n \alpha\)
Answer & Solution
Correct Answer
(D) \(2 \cos n \alpha\)
Step-by-step Solution
Detailed explanation
We have, \(x+\frac{1}{x}=2 \cos \alpha\) \(\Rightarrow \quad x^{2}+1=2 x \cos \alpha\) \(\Rightarrow \quad x^{2}-(2 \cos \alpha) x+1=0\) \(\Rightarrow \quad x=\frac{2 \cos \alpha \pm \sqrt{4 \cos ^{2} \alpha-4}}{2}\) \(=\frac{2 \cos \alpha \pm \sqrt{-4 \sin ^{2} \alpha}}{2}\)…
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