how do I prove two graphs are equivalent? (1 Viewer)

[h_s_r11]

I need to prove that P(x)= 6cos(2x)cos(2x) and R(x) = 3(cos(4x)+1) are equivalent

 

[ss2000]

First write the left side as P(x)=6cos2(2x) then use the double-angle identity :

Cos(2x) = 2cos2(x) – 1 --> cos2(x) = (1 + cos(2x))/2

Apply to cos2(2x) --> cos2(2x) = (1 + cos(4x))/2

Substitue in P(x) :

P(x) = 6(1 + cos(4x))/2 = 3(1+cos(4x)) = R(x)