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(a^2 + b^2) \sin (A - B) = (a^2 - b^2) \sin (A + B)

Source: Polish MO second round 1951 p5

August 28, 2024
geometrytrigonometry

Problem Statement

Prove that if the relationship between the sides and opposite angles A A and B B of the triangle ABC ABC is (a2+b2)sin⁡(A−B)=(a2−b2)sin⁡(A+B) (a^2 + b^2) \sin (A - B) = (a^2 - b^2) \sin (A + B) then such a triangle is right-angled or isosceles.
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