Нужно доказать тождество

Решите задачу:

$\frac{tg(a)}{1-tg^2(a)} * \frac{ctg^2(a) - 1}{ctg(a)} = \frac{ \frac{sin(a)}{cos(a)} }{1- \frac{sin^2(a)}{cos^2(a)} } * \frac{ \frac{cos^2(a)}{sin^2(a)} - 1}{ \frac{cos(a)}{sin(a)} }=$ $\frac{ \frac{sin(a)}{cos(a)} }{ \frac{cos^2(a)-sin^2(a)}{cos^2} }* \frac{ \frac{cos^2(a)-sin^2(a)}{sin^2(a)} }{ \frac{cos(a)}{sin(a)} } = \frac{sin(a)cos^2(a)(cos^2(a)-sin^2(a))sin(a)}{cos(a)*(cos^2(a)-sin^2(a))sin^2(a)cos(a)}$ $= \frac{sin^2(a)cos^2(a)}{sin^2(a)cos^2(a)}=1$