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Question

Find the value of sin2π10+sin24π10+sin26π10+sin29π10

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Solution

sin2π10+sin24π10+sin26π10+sin29π10

=sin218+sin272+sin2108+sin2162

=sin218+sin2(9018)+sin2(90+18)+sin2(18018)

=sin218+cos218+cos218+sin218

=2sin218+2cos218

=2(sin218+cos218)

=2×1

=2

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