SOLUTION: Write cos^4(3x) in terms of cosines all to the 1st power. FIND LCD & SIMPLIFY! I GOT cos^4(3x) as (cos^2(3x))^2. By solving cos(2x) = 2cos^2(x)

SOLUTION: Write cos^4(3x) in terms of cosines all to the 1st power. FIND LCD & SIMPLIFY! I GOT cos^4(3x) as (cos^2(3x))^2. By solving cos(2x) = 2cos^2(x) - 1 for cos^2(x), we get cos^2(x)

Question 759256: Write cos^4(3x) in terms of cosines all to the 1st power. FIND LCD & SIMPLIFY!
I GOT cos^4(3x) as (cos^2(3x))^2. By solving cos(2x) = 2cos^2(x) - 1 for cos^2(x), we get cos^2(x) = 1/2+1/2*cos(2x). Thus, cos^2(3x) = 1/2+1/2*cos(6x), and (cos^2(3x))^2 = 1/4 + 1/2*cos(6x) + 1/4*cos^2(6x). Next, cos^2(6x) = 1/2+1/2*cos(12x), so 1/4 + 1/2*cos(6x) + 1/4*cos^2(6x) = 1/4 + 1/2*cos(6x) + 1/8 + 1/8*cos(12x) = 3/8 + 1/2*cos(6x) + 1/8*cos(12x).
BUT IM NOT SURE PLEASE HELP!!!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Write cos^4(3x) in terms of cosines all to the 1st power.
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=
from Wikipedia half-angle formula

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