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Question

Solve sin2π4+sin23π4+sin25π4+sin27π4

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Solution

We know, that sin3π4=sin(π2+π4)=cosπ4sin5π4=sin(3π2π4)=cosπ4sin7π4=sin(2ππ4)=sinπ4

Now, sin2π4+sin23π4+sin25π4+sin27π4=sin2π4+cos2π4+cos2π4+sin2π4=1+1=2

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