\frac{1-cot ^{2}}{1+cot ^{2}} =sin ^{2} - cos^{2}
\frac{1- \frac{cos ^{2} }{sin ^{2} } }{csc ^{2} } =sin ^{2} - cos^{2}
\frac{sin ^{2}-cos ^{2} }{sin ^{2} } * sin^{2} =sin ^{2} - cos^{2}
sin ^{2} - cos^{2} =sin ^{2} - cos^{2}
pythagorian,division and reciprocal identity
