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sin^2 A+sin^2 B +sin^2 c=2 iff ABC is right triangle

Source: Polish MO Finals 1950 p5

September 1, 2024
trigonometrygeometryright triangleright angle

Problem Statement

Prove that if for angles A,B,CA,B,C of a triangle holds sin⁡2A+sin⁡2B+sin⁡2C=2\sin^2 A+\sin^2 B +\sin^2 C=2 iff the triangle ABCABC is right.
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