Prove the double angle formula through the following method

[needingtoknow]

Homework Statement

I have to prove that sin^2(a/2) = (1-cosa)/(2)

cosa = cos(2*(a/2)) = 1 -2sin^2(a/2)

I don't understand this step that was given in the solutions how do I get it?

 

[tia89]

Assuming it is clear to you that $2*\frac{\alpha}{2}=\alpha$, the equality is obtained using the formula for $\cos(2\beta)$ with $\beta=\frac{\alpha}{2}$

 

[needingtoknow]

Yes I understand that they have used the double angle formulas to derive hence cos(2*(a/2)). So the formulas for it is then cos2a = cos^2(a) - sin^2(a), so does that mean I have to do [cos(a/2)]^2 - [sin(a/2)]^2 or what then? That is what is confusing me.

 

[tia89]

First of all, don't use all the same letter, otherwise you will be confused about who is who in like a second... this is always good rule in math...
Now assuming b=a/2, you have cos(2b)=cos^2(b)-sin^2(b) indeed... now you can use the fundamental formula cos^2(b)+sin^2(b)=1 and express cos(2b) only as function of the sin^2(b). Done this, all is straightforward replacing b with a/2