[tex]\displaystyle\bf\\1)\\\\\Big(\frac{1}{Cos\alpha } -tg\alpha \Big)\Big(\frac{1}{Cos\alpha } +tg\alpha \Big)-1=\Big(\frac{1}{Cos\alpha }\Big)^{2} -\Big(tg\alpha \Big)^{2} -1=\\\\\\=\frac{1}{Cos^{2} \alpha } -tg^{2} \alpha \Big-1=tg^{2}\alpha +1-tg^{2}\alpha -1=0[/tex]

[tex]\displaystyle\bf\\2)\\\\\Big(\frac{1}{Sin\alpha } -Ctg\alpha \Big)\Big(\frac{1}{Sin\alpha } +Ctg\alpha \Big)-1=\Big(\frac{1}{Sin\alpha }\Big)^{2} -\Big(Ctg\alpha \Big)^{2} -1=\\\\\\=\frac{1}{Sin^{2} \alpha } -Ctg^{2} \alpha \Big-1=Ctg^{2}\alpha +1-Ctg^{2}\alpha -1=0[/tex]

При решении были применены формулы :

[tex]\displaystyle\bf\\tg^{2} \alpha +1=\frac{1}{Cos^{2}\alpha } \\\\\\Ctg^{2} \alpha +1=\frac{1}{Sin^{2}\alpha }[/tex]