Mathematics - Properties of Triangle Question with Solution | TestHub

The mean is -[sin $\alpha$+sin $\beta$+sin $\gamma$]/3. For $\alpha$+$\beta$+$\gamma$=2$\pi$, sin $\alpha$+sin $\beta$+sin $\gamma$=4sin($\alpha$/2)sin($\beta$/2)sin($\gamma$/2). The product of three sines with positive half-angles summing $\pi$ is at most ($\sqrt{3}$/2)³, equality $\alpha$=$\beta$=$\gamma$=2$\pi$/3. Minimum is -(4/3)($\sqrt{3}$/2)³=-$\sqrt{3}$/2.