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Question

Simplify:
sin36.sin27.sin108.sin144=516.

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Solution

sin36°sin72°sin108°sin144°

=sin36°sin72°sin(180°72°)sin(180°36°)

=sin36°sin72°sin(90°2)72°sin(90°2)36°

=sin36°sin72°sin72°sin36°

=sin236°sin272°

=[10254]2[10+254]2

=[102516][10+2516]

=(10020)(16×16)

=80(16×16)

=516(Proved)

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