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trig, absolute value equation

Source: Ukraine 1998 Grade 10 P1

June 5, 2021
trigonometryabsolute valuealgebraequation

Problem Statement

Find all pairs of real numbers (x,y)(x,y) satisfying the equation sin⁡2x+sin⁡2y=∣x∣x+∣y∣y.\sin^2x+\sin^2y=\frac{|x|}x+\frac{|y|}y.
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