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
