text: (cosx/1+sinx) + (1+sinx/cosx)\n(cos^2 x)/ (1 + sinx)(cosx) + (1 + sinx)^2\n(cos^2 x + 1 + 2sinx + sin ^2 x) / (cosx + cosxsinx)\nthen cos^2 x + sin ^2 x = 1, so substitute and you get\n(2 + 2sinx) / (cosx + cosxsinx\nthen factor a 2 out of the top, and the cosx from the bottom and you get\n(2(1+sinx)) / cosx(1+sinx)\nsimplify and you're left with\n2 / cosx\nand secx = 1/cosx\nso you get 2secx