Sprawdź podane tożsamości.    a) [latex]frac{1 - sin alpha }{sin alpha} cdot frac{1 + sin alpha}{cos alpha} = ctg alpha [/latex]     b) [latex]sin ^4 alpha - cos ^4 alpha = sin ^2 alpha - cos ^2 alpha [/latex]

a)   [latex]L=frac{1 - sin alpha }{sin alpha} cdot frac{1 + sin alpha}{cos alpha} = frac{(1-sin alpha)(1+sin alpha)}{sin alpha cos alpha}=frac{1-sin^2 alpha}{sin alpha cos alpha}= [/latex]   [latex]=frac{cos^2 alpha}{sin alpha cos alpha}=frac{cos alpha}{sin alpha}=ctg alpha=P[/latex]   b)   L = sin⁴ α - cos ⁴α = (sin²α - cos²α)(sin²α + cos²α) = (sin²α - cos²α)*1=sin²α - cos²α=P

a)   [latex]L=frac{1-sinalpha}{sinalpha}cdotfrac{1+sinalpha}{cosalpha}=frac{(1-sinalpha)(1+sinalpha)}{sinalphacdot cosalpha}=\=frac{1-sin^2alpha}{sinalpha cdot cosalpha}=[/latex] [latex]frac{cos^2alpha}{sinalphacdot cosalpha}=\=frac{cosalpha}{sinalpha}=ctgalpha=P[/latex]   b)    [latex]L=sin^4alpha-cos^4alpha=(sin^2alpha+cos^2alpha)(sin^2alpha-cos^2alpha)=\=(1-cos^2alpha+cos^2alpha)(sin^2alpha-cos^2alpha)=1cdot(sin^2alpha-cos^2alpha)=\=sin^2alpha-cos^2alpha=P[/latex]