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Question
Prove that:
cos1° cos2° cos3° ... cos180° = 0
Sum
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Solution
LHS \[ = \cos1^\circ \cos2^\circ \cos3^\circ . . . \cos180^\circ \]
\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times \cos90^\circ \times . . . \cos180^\circ \]
\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times 0 \times . . . \cos180^\circ \]
= 0
= RHS
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