Sin^2t-1/cos^4t+tg^2t

(Sin^2t - 1)/cos^4t + tg^2t = (sin^2t - 1)/cos^4t + sin^2t/cos^2t = (sin^2t - 1 + sin^2tcos^2t)/cos^4t = (sin^2t - cos^2t - sin^2t + sin^2tcos^2t)/cos^4t = (-cos^2t + sin^2tcos^2t)/cos^4t = (-cos^2t(1 - sin^2t))/cos^4t = - ((1 - sin^2t)/cos^2t) = -cos^2t/cos^2t = -1.