Say we have an angle $c$. Prove that for two angles $a$ and $b$ such that $a + b = c$,$$\sin{a}\sin{b}$$ is maximized when $$a = b = \frac{c}{2}$$
2026-03-29 16:50:19.1774803019
Maximize product of two sines given sum of angles
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Use the trigonometric sum-product relation:
$2\sin(a)\sin(b)=\cos(a-b)-\cos(a+b).$
Continue from there.