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Question

The value of cos12cos24cos36 cos48cos72cos84 is

A
164
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B
132
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C
116
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D
1128
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Solution

The correct option is A 164
Using identity {2sinθcosθ=sin2θ}
a=cos12cos24cos36cos48cos72cos84
a=(2sin12cos12)cos24cos36cos48cos72cos842sin12
a=2sin24cos24cos36cos48cos72cos844sin12
a=2sin48cos48cos36cos72cos(18084)8sin12
a=2sin96cos96cos36cos7216sin12
a=sin192cos36cos7216sin12=sin(180+12)cos36cos7216sin12
a=sin12(2sin36cos36)cos7232sin12sin36=2sin72cos7264sin36
a=sin14464sin36=sin(180144)64sin36=164
Hence, option 'A' is correct.

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