Hi I have another area problem

r = 3cos x and r = 1 + cos x

so A i= integral sign (S) a= 0; b=pi/3 ((3cos x)^2 - (1+cos x)^2) dx

which works out to S a=0;b= pi/3 (8cos^2 x - 2 cos x - 1) dx

This one is actually in my answer sheet and it gives the next step as

S a=0; b=pi/3 (4(1+cos 2x) - 2 cos x - 1) dx

Where does the 4(1+cos 2x) from????

Insight is appreciated

Calculus Beginner