Номер 1057

Доказать тождество: 1) $\frac{\cos2\alpha}{\sin\alpha\cos\alpha+\sin^2\alpha}=\operatorname{ctg}\alpha-1$; 2) $\frac{\sin2\alpha-2\cos\alpha}{\sin\alpha-\sin^2\alpha}=-2\operatorname{ctg}\alpha$; 3) $\operatorname{tg}\alpha(1+\cos2\alpha)=\sin2\alpha$; 4) $\frac{1-\cos2\alpha+\sin2\alpha}{1+\cos2\alpha+\sin2\alpha}\operatorname{ctg}\alpha=1$; 5) $\frac{(1-2\cos^2\alpha)(2\sin^2\alpha-1)}{4\sin^2\alpha\cos^2\alpha}=\operatorname{ctg}^22\alpha$; 6) $1-2\sin^2(\frac\pi4-\frac\alpha2)=\sin\alpha$; 7) $\frac{\sin\alpha+\sin2\alpha}{1+\cos\alpha+\cos2\alpha}=\operatorname{tg}\alpha$.