נושא : שימוש בזהויות 1 + tan 2 α 1 + c o t 2 α = tan 2 α ? 1 + tan 2 α = 1 cos 2 α cot 2 α = 1 sin 2 α 1 cos 2 α ∗ sin 2 α 1 = tan α s i n 2 α c o s 2 α = tan 2 α ( s i n α c o s α ) 2 = tan 2 α s i n α c o s α = tan α tan 2 = tan 2 α {\displaystyle {\begin{aligned}&{\frac {1+\tan ^{2}\alpha }{1+cot^{2}\alpha }}=\tan ^{2}\alpha ?\\&\color {blue}1+\tan ^{2}\alpha ={\frac {1}{\cos ^{2}\alpha }}\\&\color {blue}\cot ^{2}\alpha ={\frac {1}{\sin ^{2}\alpha }}\\&{\frac {1}{\cos ^{2}\alpha }}*{\frac {\sin ^{2}\alpha }{1}}=\tan \alpha \\&{\frac {sin^{2}\alpha }{cos^{2}\alpha }}=\tan ^{2}\alpha \\&\left({\frac {sin\alpha }{cos\alpha }}\right)^{2}=\tan ^{2}\alpha \\&\color {blue}{\frac {sin\alpha }{cos\alpha }}=\tan \alpha \\&\tan ^{2}=\tan ^{2}\alpha \\\end{aligned}}}
