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Question

Prove that :
cos2π15cos4π15cos8π15cos16π15=116

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Solution

cos2π15.cos4π15.cos8π15.cos16π15
=sin24.2π1516.sin2π15=sin3π1516sin2π15=sin(2π+2π15)16sinπ15
=sin2π/1516sin2π/15
=116

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