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Question

The value of cos12cos24cos36cos48cos60cos72cos84 is
  1. 164
  2. 1128
  3. 1512
  4. 1256


Solution

The correct option is B 1128
cos12cos24cos36cos48cos60cos72cos84=(cos12cos72cos48)cos60(cos24cos84cos36)=12(cos12cos(60+12)cos(6012))(cos24cos(60+24)cos(6024))=12[14cos(3×12)×14cos(3×24)]=132(cos36cos72)=132×5+14×514=1128

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