prove that (cotx+tanx)(cotx-tanx) = 1/(sin^2 x) - 1/(cos^x)
cot^2 - tan^2
cos^2/sin^2 - sin^2/cos^2
(1 - sin^2)/sin^2 - (1-cos^2)/cos^2
1/sin^2 - 1 - 1/cos^2 + 1
1/sin^2 - 1/cos^2
cos^2/sin^2 - sin^2/cos^2
(1 - sin^2)/sin^2 - (1-cos^2)/cos^2
1/sin^2 - 1 - 1/cos^2 + 1
1/sin^2 - 1/cos^2