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given trigonometric equality, find angle

Source: LIMIT 2019 CAS2 P11

April 28, 2021
geometrytrigonometry

Problem Statement

∠A,∠B,∠C\angle A,\angle B,\angle C are angles of a triangle such that sin⁡2A+sin⁡2B=sin⁡2C\sin^2A+\sin^2B=\sin^2C, then ∠C\angle C in degrees is equal to <spanclass=′latex−bold′>(A)</span> 30<span class='latex-bold'>(A)</span>~30 <spanclass=′latex−bold′>(B)</span> 90<span class='latex-bold'>(B)</span>~90 <spanclass=′latex−bold′>(C)</span> 45<span class='latex-bold'>(C)</span>~45 <spanclass=′latex−bold′>(D)</span> none of the above<span class='latex-bold'>(D)</span>~\text{none of the above}
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