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cos of a,b,(a+b) rational if sines rational (VII Soros Olympiad 2000-01 R1 10.2)

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July 28, 2021
trigonometryalgebrarational

Problem Statement

Let aa and b b be acute corners. Prove that if sin⁡a\sin a, sin⁡b\sin b, and sin⁡(a+b)\sin (a + b) are rational numbers, then cos⁡a\cos a, cos⁡b\cos b, and cos⁡(a+b)\cos (a + b) are also rational numbers.
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