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Question

Prove the following identities:
cos2π8+cos23π8+cos25π8+cos27π8=2

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Solution

L.H.S.

sin2π8+sin23π8+sin25π8+sin27π8

=sin2π8+sin23π8+sin2(π3π8)+sin2(ππ8)

=sin2π8+sin23π8+cos23π8+cos2π8

=(sin2π8+cos2π8)+(sin23π8+cos23π8)

=1+1=2

R.H.S.

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