Since
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)} = {\mathtt{cosxcosy}}{\mathtt{\,-\,}}{\mathtt{sinxsiny}}$$
and 2x=x + x
you have
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)} = {\mathtt{cosxcosx}}{\mathtt{\,-\,}}{\mathtt{sinxsinx}}$$
that is
cos(2x)=(cosx)^2-(sinx)^2
Since
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)} = {\mathtt{cosxcosy}}{\mathtt{\,-\,}}{\mathtt{sinxsiny}}$$
and 2x=x + x
you have
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)} = {\mathtt{cosxcosx}}{\mathtt{\,-\,}}{\mathtt{sinxsinx}}$$
that is
cos(2x)=(cosx)^2-(sinx)^2
