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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
