The problem is:
If one side and the opposite angle of a triangle are fixed, and the other two sides are variable, use the law of cosines to show that the area is a maximum when the triangle is isosceles.
I know that, if I let $c$ denote the fixed side and $\theta$ the angle opposite to $c$, then area $A=1/2 ab \sin{\theta}$, where $a$ and $b$ are the variable sides. I've tried substituting $b$ by the expression for it determined by the law of cosines, but that didn't seem to get me anywhere.