I know (1-cos^{2}(x/2))^{1/2}/(1-cosx)^{1/2} Is equal to 1/root2 but I don't know a formal method for justifying this, so I'm asking for someone to show me how to show my teacher that it's a true identity

I know (1-cos^{2}(x/2))^{1/2}/(1-cosx)^{1/2} Is equal to 1/root2 but I don't know a formal method for justifying this, so I'm asking for someone to show me how to show my teacher that it's a true identity