Cos(a-п)*ctg(a+п/2)*sin(4п-а)/sin(7п+а)*ctg(3п/2-а)

Cos(a-п)*ctg(a+п/2)*sin(4п-а)/sin(7п+а)*ctg(3п/2-а)

$\frac{cos( \alpha - \pi )*ctg( \alpha + \frac{ \pi }{2} )*sin(4 \pi - \alpha )}{sin(7 \pi + \alpha )*ctg( \frac{3 \pi }{2} - \alpha )} = \\ \\ \frac{cos ( \pi - \alpha )*ctg( \frac{ \pi }{2} + \alpha )*sin(- \alpha )}{sin(\pi + \alpha )*ctg( \frac{3 \pi }{2} - \alpha )} = \\ \\ \frac{-cos\alpha * (-tg\alpha) * (-sin \alpha )}{-sin\alpha *tg \alpha} = cos \alpha$