Jeśli α jest kątem rozwartym i tgα= -5, to ile wynosi wartość wyrażenia [latex] frac{1 - sin^{2} alpha }{1 - cos^{2} alpha } [/latex] ??? Z obliczeniami, proszę.

[latex]tg alpha= -5[/latex] [latex]tg alpha=frac{sinalpha}{cosalpha}[/latex] [latex]frac{sinalpha}{cosalpha}=-5[/latex] [latex]sinalpha=-5cosalpha[/latex] ------------------ [latex]sin^2alpha+cos^2alpha=1[/latex] [latex](-5cosalpha)^2+cos^2alpha=1[/latex] [latex]25cos^2alpha+cos^2alpha=1[/latex] [latex]26cos^2alpha=1 /:26[/latex] [latex]cos^2alpha=frac{1}{26}[/latex] ======================= [latex]frac{1 - sin^{2} alpha }{1 - cos^{2} alpha }=frac{cos^{2} alpha }{1 - cos^{2} alpha }=frac{frac{1}{26}}{1 -frac{1}{26}}=frac{frac{1}{26}}{frac{25}{26}}= frac{1}{25}[/latex]