I have this equation: y(t)=[A+m(t)]cos^2(wt)

I going to use the power reduction identity cos^2a=(1+cos2a)/2

I'm not sure how to handle the coefficient [A+m(t)], is a more general form of the identity: Bcos^2(a)=(B+Bcos2a)/2

So my solution would be?

y(t)=[A+m(t)]/2 + [A+m(t)]cos^2(wt)/2

If someone could clarify this, I would appreciate it, thanks.