Sprawdź tożsamość trygonometryczną

[dwukwiat15]

\(\displaystyle{ \frac{4cos2x}{ctg^{2}x-tg^{2}x}=sin^{2}2x}\)

[Piotrek89]

\(\displaystyle{ \frac {4(1-2sin^{2}x)}{(\frac {cosx}{sinx}-\frac {sinx}{cosx})(\frac {cosx}{sinx}+\frac {sinx}{cosx})} = 4(1-2sin^{2}x) * \frac {sin^{2}xcos^{2}x}{cos^{2}x-sin^{2}x}=4sin^{2}xcos^{2}x=sin^{2}2x}\)