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Question

# The value of cos12∘cos24∘cos36∘ cos48∘cos72∘cos84∘ 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 164Using identity {∵2sinθcosθ=sin2θ}a=cos12cos24cos36cos48cos72cos84⇒a=(2sin12cos12)cos24cos36cos48cos72cos842sin12⇒a=2sin24cos24cos36cos48cos72cos844sin12⇒a=−2sin48cos48cos36cos72cos(180−84)8sin12⇒a=−2sin96cos96cos36cos7216sin12⇒a=−sin192cos36cos7216sin12=−sin(180+12)cos36cos7216sin12⇒a=sin12(2sin36cos36)cos7232sin12sin36=2sin72cos7264sin36⇒a=sin14464sin36=sin(180−144)64sin36=164Hence, option 'A' is correct.

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