נושא : שימוש בזהויות1+tan2α1+cot2α=tan2α?1+tan2α=1cos2αcot2α=1sin2α1cos2α∗sin2α1=tanαsin2αcos2α=tan2α(sinαcosα)2=tan2αsinαcosα=tanαtan2=tan2α{\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}}}