Trigonometric Identities Question 310
Question: If $ \cos \theta =\frac{1}{2}( a+\frac{1}{a} ), $ then the value of $ \cos 3\theta $ is
[MP PET 2001; Pb. CET 2002]
Options:
A) $ \frac{1}{8}( a^{3}+\frac{1}{a^{3}} ) $
B) $ \frac{3}{2}( a+\frac{1}{a} ) $
C) $ \frac{1}{2}( a^{3}+\frac{1}{a^{3}} ) $
D) $ \frac{1}{3}( a^{3}+\frac{1}{a^{3}} ) $
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Answer:
Correct Answer: C
Solution:
$ \because \ \cos 3\theta =4{{\cos }^{3}}\theta -3\cos \theta $
$ \therefore \cos 3\theta =4\frac{1}{2^{3}}{{( a+\frac{1}{a} )}^{3}}-3\frac{1}{2}( a+\frac{1}{a} ) $
$ \Rightarrow \cos 3,\theta =\frac{1}{2}( a+\frac{1}{a} ),[ {{( a+\frac{1}{a} )}^{2}}-3 ] $
Þ $ \cos 3\theta =\frac{1}{2}( a^{3}+\frac{1}{a^{3}} ) $ .
BETA
