Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013

Tags: algebra, equation, trigonometry



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