The triangle ABC has sides of length, a,b and c, as shown in the diagram. The point D lies on AB and CD is perpendicular to AB.

a) Show that asinB = bsinA.

b) Show that c = acosB + bcosA.

c) Given that c^2 = 4ab cosA cos B, show that a=b.

Could someone please show me how to do (c) of the question?

I've tried equating (b) squared to (c) but I end up with asinB = b sinA. How do I use this to prove a=b?