Write (Cos(5x))^2 using half angle formula

I need to know how to write some thing like (Cos(5x))^2 using a half angle formula, Such that I have something that looks like

(Cos(5x))^2=_______+_______cos(___x)

I know with a half angle formula that

Cos(x/2)=+/- sqrt((1+cos(x))/2)

but that ^2 is throwing me off, I don't know what to do with it per se.

Would something like = +/- sqrt((1+cos(5x)^2)/2)

Then using a power reducing formula work?

cos(x)^2=(1+cos2x)/(2)

\sqrt{\frac{1+\cos\!\left(\frac{2\cdot 5x}{2}\right)}{2}}" alt="\sqrt{\frac{1+\cos\!\left(\frac{2\cdot 5x}{2}\right)}{2}}" />

(i do not know why font is coming up)

I'm not sure what to do with 5x if I'm supposed to end up with 2x

would it be cos(2(5x)) or am I going down the wrong path?

Any suggestions?

Thank you for your time.