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Calculate the product of sines - [Iran Second Round 1987]

Source:

December 23, 2010
trigonometryalgebra proposedalgebra

Problem Statement

Calculate the product: A=sin⁡1∘×sin⁡2∘×sin⁡3∘×⋯×sin⁡89∘A=\sin 1^\circ \times \sin 2^\circ \times \sin 3^\circ \times \cdots \times \sin 89^\circ
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