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MMO 178 Moscow MO 1950 sinx =(sinBsinC)/(1 - cosB cosCcosA)

Source:

August 6, 2019
trigonometryangles

Problem Statement

Let AA be an arbitrary angle,let BB and CC be acute angles. Is there an angle xx such that sinx=sinBsinC1cosBcosCcosA?\sin x =\frac{\sin B \cdot \sin C}{1 - \cos B \cdot \cos C \cdot \cos A} ?