Question

simplify cos(nx)*cos(x)-sin(nx)*sin(x)

Answer 1

\[\cos(nx)\cos(x)-\sin(nx)\sin(x)\]

Answer 2

\[
\cos a\cos b-\sin a\sin b=\cos[a+b]\\
\cos nx\cos x-\sin nx\sin x=\cos[nx+x]=cos[x(n+1)]
\]

Answer 3

dude you are a genius.. thanks man