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With the help of the Pythagorean identity, we can express cosv in terms of sinv,
cos2v+sin2v=1cosv=1−sin2v.
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
cosv=
1−sin2v. 
2