Udowodnij tożsamości trygonometryczne: Bardzo proszę o pomoc

a) [latex]sinalpha(sinalpha+tgalphacdot cosalpha)=sinalpha(sinalpha+frac{sinalpha}{cosalpha}cdot cosalpha)=\ sinalphacdot2sinalpha=2sin^2alpha[/latex]   b) [latex]frac{1-cos^2alpha}{cosalphacdot sinalpha}=frac{sin^2alpha}{cosalphacdot sinalpha}=frac{sinalpha}{cosalpha}=tgalpha[/latex]   c) [latex]frac{sinalpha-sin^3alpha}{cosalpha-cos^3alpha}=frac{sinalpha(1-sin^2alpha)}{cosalpha(1-cos^2alpha)}=frac{sinalphacdot cos^2alpha}{cosalphacdot sin^2alpha}=frac{cosalpha}{sinalpha}=tgalpha[/latex]    

[latex][1. sinalpha*(sinalpha+tgalpha*cosalpha)=2sin^{2}alpha \ sinalpha*(sinalpha+frac{sinalpha}{cosalpha}*cosalpha)=2sin^{2}alpha \ sinalpha*(sinalpha+sinalpha)=2sin^{2}alpha \ sinalpha*2sinlpha=2sin^{2}alpha \ 2sin^{2}alpha=2sin^{2}alpha \ L=P \ 2. frac{1-cos^{2}alpha}{cosalpha*sinalpha}=tgalpha --> sin^{2}alpha+cos^{2}alpha=1 \ frac{sin^{2}alpha+cos^{2}alpha-cos^{2}alpha}{cosalpha*sinalpha}=tgalpha \ frac{sin^{2}alpha}{cosalpha*sinalpha}=tgalpha \[/latex] [latex]frac{sinalpha}{cosalpha}=tgalpha \ 3. frac{sinalpha-sin^{3}alpha}{cosalpha-cos^{3}alpha}=ctgalpha \ frac{sinalpha*(1-sin^{2}alpha)}{cosalpha*(1-cos^{2}alpha)}=ctgalpha \ frac{sinalpha*cos^{2}alpha}{cosalpha*sin^{2}alpha}=ctgalpha \ frac{cosalpha}{sinalpha}=ctgalpha[/latex]