Sprawdź tożsamość(sin[latex] alpha [/latex]+2cos[latex] alpha [/latex])²+(2sin[latex] alpha [/latex]-cos[latex] alpha [/latex]²=4

[latex](sinalpha +2cos alpha )^2+(2sin alpha -cos alpha)^2=4[/latex] [latex]L=(sinalpha +2cos alpha )^2+(2sin alpha -cos alpha)^2=[/latex] [latex]sin^2alpha +4sinalpha cos alpha+4cos^2alpha+4sin^2alpha-4sinalpha cos alpha+cos^2alpha=[/latex] [latex]1+4sin^2alpha+4cos^2alpha=[/latex] [latex]1+4(sin^2alpha+cos^2alpha)=1+4 cdot 1=1+4=5 eq P[/latex]