Trigonometric Identities Question 195
Question: If $ \cos \alpha +\cos \beta =0=sin\alpha +sin\beta , $ then $ \cos 2\alpha +\cos 2\beta $ is equal to
Options:
A) $ -2\sin (\alpha +\beta ) $
B) $ -2\cos (\alpha +\beta ) $
C) $ 2\sin (\alpha +\beta ) $
D) $ 2\cos (\alpha +\beta ) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ {{(cos\alpha +cos\beta )}^{2}}-{{(sin\alpha +sin\beta )}^{2}}=0 $ Or $ (cos^{2}\alpha +cos^{2}\beta +2\cos \alpha \cos \beta ) $ $ -(sin^{2}\alpha +sin^{2}\beta +2\sin \alpha \sin \beta )=0 $ Or $ \cos 2\alpha +\cos 2\beta =-2(cos\alpha \cos \beta -\sin \alpha \sin \beta ) $ $ =-2\cos (\alpha +\beta ) $
BETA
