Question

Solve: cos(x)(cos(x)-1)=0

Answer 1

\(\large {
cos(x)[cos(x)-1]=0\implies
\begin{cases}
cos(x)=0
\\ \quad \\
cos(x)-1=0
\end{cases}
}\)

solve for cos(x)
but that pretty much gives you 2 conspicuous values
0 and 1

so check your unit circle, see what angles meet that
in the notation, I assume "n" stands for an integer, or \(\bf n \in \mathbb{Z}\)