With the help of the Pythagorean identity, we can express
cosv
in terms of
sin v,
cos2v+sin2v=1
In addition, we know that the angle
v
lies between
−2
and
2, i.e. either in the first or fourth quadrant, where angles always have a positive
x
-coordinate (cosine value); thus, we can conclude that
2
1−sin2 v=
1−a2 