Thread: Gauss Bonnet theorem for hyperbolic triangle

Hi, i was hoping that someone could help me understand the integration parts of the proof on page 3 of: http://www.maths.manchester.ac.uk/~c.../lecture07.pdf
Particularly i dont understand where the sqrt(1-x^2) comes from on the integral and the beta and pi - alpha

The square roor comes from the convention that one side of the triangle is part of the unit circle, while alpha and beta come from the change of variables in the integral.