Trigonometric Identities Question 154
Question: If $ x+\frac{1}{x}=2\cos \alpha $ , then $ x^{n}+\frac{1}{x^{n}}= $
[Karnataka CET 2004]
Options:
A) $ 2^{n}\cos \alpha $
B) $ 2^{n}\cos n\alpha $
C) $ 2i,\sin ,n,\alpha $
D) $ 2\cos ,n\alpha $
Show Answer
Answer:
Correct Answer: D
Solution:
We have, $ 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 $ Similarly $ x^{n}+\frac{1}{x^{n}}=2\cos ,n\alpha $ .
BETA
