Trigonometric Identities Question 304

Question: If $ \cos 3\theta =\alpha \cos \theta +\beta {{\cos }^{3}}\theta , $ then $ (\alpha ,\beta )= $

Options:

A) $ (3,,4) $

B) $ (4,,3) $

C) $ (-3,,4) $

D) $ (3,,-4) $

Show Answer

Answer:

Correct Answer: C

Solution:

Given that $ \cos 3\theta =\alpha \cos \theta +\beta {{\cos }^{3}}\theta $ But $ \cos 3\theta =4{{\cos }^{3}}\theta -3\cos \theta $
Þ $ (\alpha ,\beta )=(-3,,4) $ .