$ tan(2α) (sin(α) - cos(α) + \frac{sin^2(α)}{cos(α)} - sin(α))$
$ tan(2α) ( - cos(α) + \frac{sin^2(α)}{cos(α)})$
$ \frac{2tan(α)}{1-tan^2(α)} ( \frac{sin^2(α)-cos^2(α)}{cos(α)})$
$ \frac {2 \frac{sin(α)}{cos(α)}}{1-\frac {sin^2(α)}{cos^2(α)}} ( \frac{sin^2(α)-cos^2(α)}{cos(α)})$
$ \frac {2 \frac{sin(α)}{cos(α)}}{\frac {cos^2(α) - sin^2(α)}{cos^2(α)}} ( \frac{sin^2(α)-cos^2(α)}{cos(α)})$
$ \frac {2sin(α)(sin^2(α) - cos^2(a))}{cos^2(α) - sin^2(α)} $
$ - 2 sin(α) $
Nell’ultimo passaggio come ha fatto ad avere 2sina e come denominatore cos^2