Udowodnij tożsamosc trygonometryczną: (tg2x-sin2x)ctg2x=sin2x

[latex]L = (tg^{2}x - sin^{2}x)ctg^{2}x = (frac{sin^{2}x}{cos^{2}x}-sin^{2}x)*frac{cos^{2}x}{sin^{2}x}=\\=frac{sin^{2}x}{cos^{2}x}*frac{cos^{2}x}{sin^{2}x}-sin^{2}x*frac{cos^{2}x}{sin^{2}x}=1-cos^{2}x = \\=sin^{2}x + cos^{2}x - cos^{2}x = sin^{2}x\\P = sin^{2}x\\L = P\\\\lub\L = (tg^{2}x - sin^{2}x)ctg^{2}x = tg^{2}x * ctg^{2}x - sin^{2}x *frac{cos^{2}x}{sin^{2}x} =1 - cos^{2}x=\\=sin^{2}x + cos^{2}x - cos^{2}x = sin^{2}x = P[/latex]

tg = sin/cos L=(Sin2x / cos 2x - sin 2x) Cos2x / sin2x =  1- cos 2x = sin 2x L=P