Question

prove that(1+tan^2theata)+(1+1/tan^2theata)=1/sin^2theata-sin^4theata

Answer 1

$(1 + \tan {}^{2} theta) + (1 + 1 \div \tan {}^{2} theta) = 1 \div \sin {}^{2} - \sin {}^{4} theta \\ sec {}^{2} theta + (1 + \cos {}^{2} theta \div \sin {}^{2} theta) = 1 \div \sin {}^{2} theta - \sin {}^{4} theta \\ 1 \div \cos {}^{2} theta + 1 \div \sin {}^{2} theta = 1 \div \sin {}^{2} theta - \sin ^{4} theta \\ sin ^{2} theta + \cos {}^{2} theta \div (1 - \sin {}^{2} theta)( \sin {}^{2} theta) = 1 \div \sin {}^{2} theta - \sin {}^{4} theta \\ 1 \div \sin {}^{2} theta - \sin {}^{4} theta = 1 \div \sin {}^{2} theta - \sin {}^{4} theta \\ l.h.s = r.h.s \\ thank \: you$