I need to prove that P(x)= 6cos(2x)cos(2x) and R(x) = 3(cos(4x)+1) are equivalent
h_s_r11 New Member Joined Feb 4, 2023 Messages 10 Location microwave Gender Female HSC 2025 Jun 20, 2024 #1 I need to prove that P(x)= 6cos(2x)cos(2x) and R(x) = 3(cos(4x)+1) are equivalent
S ss2000 New Member Joined May 24, 2024 Messages 13 Gender Male HSC 2000 Jun 21, 2024 #2 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)
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)
