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Question

The value of 10n=1(sin2nπ11cos2nπ11) is equal to

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Solution

S=10n=1(sin2nπ11cos2nπ11)
=(sin2π11cos2π11)+(sin4π11cos4π11)+(sin6π11cos6π11)++(sin20π11cos20π11)
=(sin2π11+sin4π11++sin20π11)(cos2π11+cos4π11++cos20π11)
=sinπsin10π11sinπ11cosπsin10π11sinπ11
=0+sin(ππ11)sinπ11
=1

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