Question

tan^2x=sec^2-sin^2x-cos^2x

Answer 1

First use the Pythagorean identity sin^2 (angle) + cos^2 (angle) = 1.

(tan^2 2x)+(sin^2 2x)+(cos^2 2x) = (sec^2 2x)
(tan^2 2x)+1 = (sec^2 2x)

Next another Pythagorean identity is that tan^2 (angle) + 1 = sec^2 (angle), so substitute...

sec^2 2x = sec^2 2x

Done!