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Regional Olympiad - FBH 2013 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

September 24, 2018
algebraequationtrigonometry

Problem Statement

Let aa and bb be real numbers from interval [0,π2]\left[0,\frac{\pi}{2}\right]. Prove that sin⁡6a+3sin⁡2acos⁡2b+cos⁡6b=1\sin^6 {a}+3\sin^2 {a}\cos^2 {b}+\cos^6 {b}=1 if and only if a=ba=b
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