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