Hensen inequality in trigonometry: $\sin A + \sin B + \sin C \leq \frac{3}{2} \cdot \sqrt[2]{3}$ [duplicate]

Can anyone help me how to prove $\sin A + \sin B + \sin C \leq \frac{3}{2} \cdot \sqrt[2]{3}$

I have idea use Jensen but how to use it here?

marked as duplicate by user26486, graydad, Hippalectryon, saz, user149792Mar 3 '15 at 19:57

• If $A=B=C=90^\circ$ then $\sin A+\sin B+\sin C=3>\dfrac 3 2 \sqrt{3}$. If you intended some hypothesis on $A,B,C$, e.g. they are the three angles in a triangle, then that should be stated. – Michael Hardy Mar 3 '15 at 15:30