No, √(1 - cos(θ - φ))/2 is correct.


How did you reformulate P and Q for that?

But I can't seem to find a simple manipulation for P and Q to get the second formula all I can find is

(P dot e₁)(Q dot e₁) - (P dot e₂)(Q dot e₂)

Where e₁ = (1,0) and e₂ = (0,1)

Again the back of my book gives the expanded for of cos([tex]\phi[/tex] + [tex]\theta[/tex]) so I don't even know what they are trying to say.