Converting between Trig Forms to Represent a Cardioid

[darkblue]

Homework Statement

Show that the cardioid r=a(1+cos(theta)) can be represented by r=2acos²(theta/2), 0<=theta<=2pi (theta is between 0 and 2pi).

Homework Equations

The Attempt at a Solution

I'm pretty sure I have to equate the two expressions, but I haven't been able to do this. Then I thought of converting both of them to cartesian form (and seeing if they have the same equation) but that's turning into a bit of a mess. Any guidance would be greatly appreciated!

 

[Tinyboss]

Those are trig functions. There are lots of identities involving trig functions. One of them might be helpful.