Uzasadnij, że dla dowolnego [latex] alpha [/latex] prawdziwa jest równość: [latex] frac{tg^{2} alpha}{tg^{2} alpha + 1 } = sin^{2} alpha [/latex]

[latex]dfrac{tg^2alpha}{tg^2alpha+1}=[/latex] [latex]dfrac{frac{sin^2alpha}{cos^2alpha}}{frac{sin^2alpha}{cos^2alpha}+1}=[/latex] [latex]dfrac{frac{sin^2alpha}{cos^2alpha}}{frac{sin^2alpha}{cos^2alpha}+frac{cos^2alpha}{cos^2alpha}}=[/latex] [latex]dfrac{frac{sin^2alpha}{cos^2alpha}}{frac{sin^2alpha+cos^2alpha}{cos^2alpha}}=[/latex] [latex]dfrac{frac{sin^2alpha}{cos^2alpha}}{frac{1}{cos^2alpha}}=[/latex] [latex]dfrac{sin^2alpha}{cos^2alpha}cdot{dfrac{cos^2alpha}{1}=[/latex] [latex]dfrac{sin^2alpha}{1}=sin^2alpha[/latex] c.b.d.u.