Expressing $\cos(x)^6$ as a linear combination of $\cos(kx)$'s Let $$(\cos^6(x)) = m\cos(6x)+n\cos(5x)+o\cos(4x)+p\cos(3x)+q\cos(2x)+r\cos(x)+a.$$ 
What is the value of $a$?

Method $1:$
Use $\displaystyle\cos3A=4\cos^3A-3\cos A\iff \cos^3A=\cdots$ for $\displaystyle\cos^6x=(\cos^3x)^2$
and $\displaystyle\cos2B=2\cos^2B-1\iff \cos^2B=\cdots$
Method $2:$
Using Euler Formula, $\displaystyle\cos y=\frac{e^{iy}+e^{-iy}}2$
