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Question

The value of cos2π8+cos23π8+cos25π8+cos27π8 is

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Solution

The given expression
12(2cos2π8+2cos23π8+2cos25π8+2cos27π8)
=12(1+cosπ4+1+cos3π4+1+cos5π4+1+cos7π4)[2cos2θ=1+cos2θ]
=12[4+cosπ4+cos(ππ4)+cos(π+π4)+cos(2ππ4)]
=12(4+cosπ4cosπ4cosπ4+cosπ4)=12×4=2

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