Despite the long title, my question is very short and clear:
Can you not just derive the surface area formula for a spherical triangle from the angle of sum formula of a spherical triangle with two simple equations?
The angle of sum formula is as follows: π+(T∆ABC/r^2)=A+B+C
And can I not just subtract pi and divide with r^2 on both sides of the equation and get the surface area formula for a spherical triangle; T∆ABC= (A+B+C- π)∙r2?