Have you expanded out the LHS? Can you apply any identities here?
I think I found the solution. Please, check it for me:
For any A, and a is maximum if and only if b=c (you can use the area= 1/2 bc sin A to approach it).
hence for a triangle with b=c:
if:
by using the derrivative of f(x), and setting f'(x)=0 we get:
Then the maximum value of f(x) ) is
now we proved that for a triangle ABC
Let's consider a function g(x) such that:
The roots of g(x) are :
Hence:
and since :
(as we proved)
Then:
-->
Thus :