Trigonometric Identities Question 210
Question: $ 1+\cos 56^{o}+\cos 58^{o}-\cos 66^{o}= $
[IIT 1964]
Options:
A) $ 2\cos 28^{o}\cos 29^{o}\cos 33^{o} $
B) $ 4\cos 28^{o}\cos 29^{o}\cos 33^{o} $
C) $ 4\cos 28^{o}\cos 29^{o}\sin 33^{o} $
D) $ 2\cos 28^{o}\cos 29^{o}\sin 33^{o} $
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Answer:
Correct Answer: C
Solution:
$ 1+\cos 56{}^\circ +\cos 58{}^\circ -\cos 66{}^\circ $
$ =2{{\cos }^{2}}28{}^\circ +2\sin 62{}^\circ .\sin 4{}^\circ $
$ =2{{\cos }^{2}}28{}^\circ +2\cos 28{}^\circ .\sin 4{}^\circ $
$ =2\cos 28{}^\circ (\cos 28{}^\circ +\cos 86{}^\circ ) $
$ =2\cos 28{}^\circ .2\cos 57{}^\circ \cos 29{}^\circ $
$ =4\cos 28{}^\circ \cos 29{}^\circ \sin 33{}^\circ $ .
BETA
