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Question

Solve:
cos6x=32cos6x48cos4x+18cos2x1

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Solution

cos6x=cos2(3x)=2cos23x1
Also, cos3x=4cos3x3cosx
cos6x=2cos23x1
=2(4cos3x3cosx)21
=2(16cos6x+9cos2x24cos4x)1
=32cos6x48cos4x+18cos2x1
Hence proved.

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