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

Answer 1

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