Question 391094
Write everything in terms of sin and cos:


{{{1/cos(x) - sin(x)*sin(x)/cos(x)}}} Add the two fractions


{{{(1 - sin^2 (x))/cos(x)}}} Since {{{1 - sin^2 (x) = cos^2 (x)}}} by the Pythagorean identity, replace the numerator with {{{cos^2 (x)}}} to obtain


{{{cos^2 (x)/cos (x)}}} which is equal to {{{cos (x)}}} provided that {{{cos (x) <> 0}}}.