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Question

The value of tan3π24tan5π24tan11π24 is equal to:

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Solution

We have,

tan3π24tan5π24tan11π24

=sin3π24sin5π24sin11π24cos3π24cos5π24cos11π24

Multiplying and divide by 2 and we get.

=2sin3π24sin5π24sin11π242cos3π24cos5π24cos11π24

=[cos(3π245π24)cos(3π24+5π24)]sin11π24[cos(3π24+5π24)+cos(3π245π24)]cos11π24

=[cosπ12cosπ3]sin11π24[cosπ3+cosπ12]cos11π24

=[cosπ1212]sin11π24[12+cosπ12]cos11π24

=[2cosπ121]sin11π24[1+2cosπ12]cos11π24

=2cosπ12sin11π24sin11π24cos11π24+2cosπ12cos11π24

=sin(π12+11π24)sin(π1211π24)sin11π24cos11π24+cos(π12+11π24)+cos(π1211π24)

=sin(13π24)sin(9π24)sin11π24cos11π24+cos(13π24)+cos(9π24)

=sin13π24+sin9π24sin11π24cos11π24+cos13π24+cos9π24

Hence, this is the answer.

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