Question

The function cos(5θ) can be written as acos^5(θ)−bcos^3(θ)+ccos(θ) where a, b, and c are positive integers. Find a+b+c.

Answer 1

put \[\theta=0,1=a-b+c\]
\[\theta=\pi,-1=-a+b+c\]

Answer 2

i mean\[\theta=\pi,-1=-a+b-c\]

\[\theta=\pi/3,1/2=a/2^5-b/2^3+c\]
\[\theta=\pi/4,2^{1/2}=a2^{-5/2}-b2^{-3/2}+c2^{-1/2}\]
\[a=16,b20,c=5,a+b+c=41\]

Answer 3

16 cos^5 (theta) - 20 cos^3 (theta) + 5 cos (theta)