Among all triangles ABC find the maximum value of \(\sin A + \sin B \sin C.\)

\(\text{The answer appears to be $\dfrac 1 2(1+\sqrt{5})$}\)

How did you reach that conclusion Rom?

set the Gradient equal to zero and solved (with the help of software) and examined the solutions to see which

produced a maximum (vice a minimum) and what it was.

There's probably some more clever geometric solution here.

Here's a possible derivation:

Thanks Rom and Alan