3.Trigonometrical Ratios, Functions and Identities
easy

यदि $x + \frac{1}{x} = 2\cos \alpha $, तो ${x^n} + \frac{1}{{{x^n}}} = $

A

${2^n}\cos \alpha $

B

${2^n}\cos n\alpha $

C

$2i\,\sin \,n\,\alpha $

D

$2\cos \,n\alpha $

Solution

(d) यहाँ  $x + \frac{1}{x} = 2\cos \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 $

इसी प्रकार  ${x^n} + \frac{1}{{{x^n}}} = 2\cos \,n\alpha $.

Standard 11
Mathematics

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