udowodnij tozsamosc trygonometryczna a) (sin x + cos x)^2+(sin x-cos x)^2=2 b) sin^4 x-cos^4 x=sin ^2x-cos^2x c) (tg^2x-sin^2x)ctg^2x=sin^2x d) (1-cos^2x)(sin x cos x)=tg x

a) [latex]sin^{2}x+2sinxcosx+cos^2x+sin^{2}x-2sinxcosx+cos^{2}x=2[/latex] [latex] 2(sin^{2}x+cos^{2}) =2[/latex] [latex] 2*1=2 [/latex] [latex] 2=2[/latex] b) [latex](sin^{2}x-cos^{2}x)(sin^{2}+cos^{2})=(sin^{2}x-cos^{2}x) [/latex] [latex](sin^{2}x-cos^{2}x)*1=(sin^{2}x-cos^{2}x)[/latex] [latex](sin^{2}x-cos^{2}x)=(sin^{2}x-cos^{2}x)[/latex] c) [latex]( frac{sin^{2}x}{cos^{2}x}-sin^{2}x )* frac{cos^{2}x}{sin^{2}x} =sin^{2}x[/latex] [latex] (1-cos^{2}x)=sin^{2}x [/latex] [latex] sin^{2}x=sin^{2}x[/latex] d) [latex] frac{sin^{2}x}{sinxcosx} =tgx[/latex]  [latex]frac{sinx}{cosx} =tgx[/latex]  [latex] tgx=tgx[/latex]