Trigonometric Identities Question 20
Question: The value of $ \cos 12{}^\circ +\cos 84{}^\circ +\cos 156{}^\circ +\cos 132{}^\circ $ is
[Kerala (Engg.) 1993]
Options:
A) $ \frac{1}{2} $
B) 1
C) $ -\frac{1}{2} $
D) $ \frac{1}{8} $
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Answer:
Correct Answer: C
Solution:
$ \cos 12^{o}+\cos 84^{o}+\cos 156^{o}+\cos 132^{o} $ $ =(\cos 12^{o}+\cos 132^{o})+(\cos 84^{o}+\cos 156^{o}) $ $ =2\cos 72^{o}\cos ,60^{o}+2\cos 120^{o}\cos 36^{o} $ $ =2,[ \cos 72^{o}\times \frac{1}{2}-\frac{1}{2}\times \cos 36^{o} ] $ $ =[\cos 72^{o}-\cos ,36^{o}] $ $ =[ \frac{\sqrt{5}-1}{4}-\frac{\sqrt{5}+1}{4} ]=\frac{-1}{2} $ .
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