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Question

The value of cotπ20cot3π20cot5π20cot7π20cot9π20 is

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Solution

Given
cotπ20cot3π20cot5π20cot7π20cot9π20=(cotπ20cot9π20)cotπ4(cot3π20cot7π20)=[cotπ20cot(π2π20)][cot3π20cot(π23π20)]=(cotπ20tanπ20)(cot3π20tan3π20)=1

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