So we have

\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)

If we multiply it by two we have

\(\displaystyle{2}{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)

Which we can say it's a sum

\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}+{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)

Which is the double angle formula of the sine

\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}+{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}={\sin{{\left({2}{x}\right)}}}\)

But since we multiplied by 2 early on to get to that, we need to divide by two to make the equality, so

\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}={\frac{{{\sin{{\left({2}{x}\right)}}}}}{{{2}}}}\)