1 + tan 2 α = 1 cos 2 α = 1 + sin 2 α cos 2 α = cos 2 α + sin 2 α cos 2 α = 1 cos 2 α {\displaystyle {\begin{aligned}1+\tan ^{2}\alpha ={\frac {1}{\cos ^{2}\alpha }}=1+{\frac {\sin ^{2}\alpha }{\cos ^{2}\alpha }}={\frac {\cos ^{2}\alpha +\sin ^{2}\alpha }{\cos ^{2}\alpha }}={\frac {1}{\cos ^{2}\alpha }}\end{aligned}}}
