wykaż tożsamość [latex] frac{1}{sin x razy cos x} [/latex]-[latex] frac{cosx}{sinx} [/latex]= tgx

[latex]frac{1}{sin xcdot cos x} - frac{cosx}{sinx} = tgx[/latex] [latex]L=frac{1}{sin xcdot cos x} - frac{cosx}{sinx}=[/latex] [latex]frac{1}{sin xcdot cos x} - frac{cosxcdot cos x}{sin xcdot cos x}=[/latex] [latex]frac{1-cos^2x}{sin xcdot cos x}=[/latex] [latex]frac{sin^2x}{sin xcdot cos x}=[/latex] [latex]frac{sinx}{cos x}=tgx=P[/latex]