Trigonometric Identities Question 156
Question: If $ \cos \theta =\frac{1}{2}( x+\frac{1}{x} ) $ , then $ \frac{1}{2}( x^{2}+\frac{1}{x^{2}} )= $
[AMU 1998]
Options:
A) $ \sin 2\theta $
B) $ \cos ,2\theta $
C) $ \tan ,2\theta $
D) $ \sec ,2\theta $
Show Answer
Answer:
Correct Answer: B
Solution:
Given that $ \cos \theta =\frac{1}{2},( x+\frac{1}{x} )\Rightarrow ,x+\frac{1}{x}=2,\cos \theta $ We know that $ x^{2}+\frac{1}{x^{2}}={{( x+\frac{1}{x} )}^{2}}-2 $ $ ={{(2\cos \theta )}^{2}}-2=4,{{\cos }^{2}}\theta -2=2,\cos 2\theta $
$ \therefore \frac{1}{2},( x^{2}+\frac{1}{x^{2}} )=\frac{1}{2}\times 2,\cos ,2\theta =\cos ,2\theta $
BETA
