MCQ
જો $x + \frac{1}{x} = 2\cos \alpha $, તો ${x^n} + \frac{1}{{{x^n}}} = $
- A${2^n}\cos \alpha $
- B${2^n}\cos n\alpha $
- C$2i\,\sin \,n\,\alpha $
- ✓$2\cos \,n\alpha $
${x^2} + \frac{1}{{{x^2}}} + 2 = 4{\cos ^2}\alpha $.
${x^2} + \frac{1}{{{x^2}}} = 4{\cos ^2}\alpha - 2$
${x^2} + \frac{1}{{{x^2}}} = 2(2{\cos ^2}\alpha - 1) = 2\cos 2\alpha $
Similarly ${x^n} + \frac{1}{{{x^n}}} = 2\cos \,n\alpha $.
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