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