Question

Упростите уравнение (А19)
С пояснением пожалуйста!

Answer 1

$\frac{Sin(\frac{9}{2}\pi -\alpha)-Ctg(5\pi+\alpha)}{Sin(\pi-\alpha)-1} =\frac{Sin[4\pi+(\frac{\pi }{2}-\alpha)]-Ctg\alpha}{Sin\alpha-1} =\frac{Sin(\frac{\pi }{2}-\alpha)-Ctg\alpha}{Sin\alpha-1 }=\frac{Cos\alpha-\frac{Cos\alpha}{Sin\alpha}}{Sin\alpha-1}=\\\\=\frac{\frac{Cos\alpha Sin\alpha-Cos\alpha}{Sin\alpha}}{Sin\alpha-1}=\frac{Cos\alpha(Sin\alpha-1)}{Sin\alpha(Sin\alpha-1)}=\frac{Cos\alpha}{Sin\alpha}=Ctg\alpha \\\\Otvet:\boxed{Ctg\alpha}$