I know \(\displaystyle sin^2(x)=\frac{1}{2}(1-\cos{(2x)})\)

I’m wondering if this formula works for any real number for the coefficient in the argument for sin(x)?

If so would it look like this? \(\displaystyle sin^2{(\alpha{x})}=\frac{1}{2}(1-=cos^2{({2}\alpha{x})})\)

Or like this? \(\displaystyle sin^2{(\alpha{x})}=\frac{1}{2\alpha}(1-=cos^2{({2}\alpha{x})})\)

Or...

Also if the coefficient can be any real number I'm assuming it works for \(\displaystyle cos^2(x)=\frac{1}{2}(1+\cos{(2x)})\) as well?

Thanks in advance.