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Question

sin2π18+sin2π9+sin27π18+sin24π9=k. Find the value of k.

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Solution

sin2π18+sin2π9+sin27π18+sin24π9
=sin2π18+sin2(π2π18)+sin2π18+sin2(π2π9)
=sin2π18+cos2(π18)+cos2(π9)+sin2π9=1+1=2

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