Question

1 - cos(6x) = _____?

Answer 1

\(\large\color{midnightblue}{ 1 - \cos(6x) }\)
\(\large\color{midnightblue}{ 1 -[~ \cos(3x+3x)~] }\)
\(\large\color{midnightblue}{ 1 - [~\cos^2(3x)-\sin^2(3x)~] }\)
\(\large\color{midnightblue}{ 1 - \cos^2(3x)+\sin^2(3x) }\)
\(\large\color{midnightblue}{ \sin^2(3x)+\sin^2(3x) }\)
\(\large\color{midnightblue}{ 2\sin^2(3x) }\)

Answer 2

you can continue to reduce it till cos(x), but this is where I would stop.