Verified answer

[tex]\displaystyle\bf\\1)\\\\\Big(Sin^{2} \alpha +tg^{2} \alpha Sin^{2}\alpha \Big) Ctg\alpha =Sin^{2} \alpha \cdot\Big(1+tg^{2} \alpha \Big) \cdot\frac{Cos\alpha }{Sin\alpha } =\\\\\\=Sin\alpha \cdot Cos\alpha \cdot \frac{1}{Cos^{2} \alpha }=\frac{Sin\alpha }{Cos\alpha } =tg\alpha \\\\\\2)\\\\\frac{Sin^{2} t-1}{Cos^{4}t } +tg^{2} t=\frac{-Cos^{2} t}{Cos^{4}t } +tg^{2}t=-\frac{1}{Cos^{2}t } +tg^{2} t=\\\\\\=-\Big(1+tg^{2} t\Big)+tg^{2} t=-1-tg^{2} t+tg^{2} t=-1[/tex]