Prove that sec^2x-cosec^2x=tan^2x-cot^2x

Use the identities sec^2(x) = tan^2(x) + 1 and cosec^2(x) = 1 + cot^2 (x), both are derived from the pythagorean identity of 1 = sin^2 (x) + cos^2 (x) by dividing through by either sin2 or cos2 .