Lesson:
double angle identities- 
    Sin(2x)=2SinxCosx
    Cos(2x)=2Cosx^2-1
                 =1-2Sin^2x
                 =Cos^2x-Sin^x
    Tan(2x)=(2Tanx)/(1-Tan^2x)
Plug the numbers into an equation and solve.

Medium example problem

Solve for Cos(2t)

Cos(2t)=Cos^2(t)-Sin^2(t)
              =Cos^2(t)-(1-Cos^2t)
              =2(Cos^2(t))-1
              =2(-7/9)^2-1
              =2(49/81)-1

Here is an easier one

y=4cos^2x-2

plug this into the equation

y=4cos^2x-2

There is a 2 taken from the 4 and the -2 which is placed in the front as so...

 =2(2cos^2x-1)

From here, remember to simplify further into...

 =2cos2x