Question

Решить первое задание.

Answer 1

$displaystyle cos (pi-alpha)=cos pi cos alpha +sin pi sin alpha=-cos alpha\\cosleft( frac{pi}{2}-alpha right)=sin alpha\\sin (2pi -alpha)=sin (-alpha+2pi)=sin (-alpha)=-sin alpha\\sin left( frac{3pi}{2}-alpha right)=sin frac{3pi}{2}cos alpha-cos frac{3pi}{2}sin alpha=-cos alpha$

Т.е. 

$displaystylefrac{-cos alpha+sin alpha}{-sin alpha+cos alpha} = frac{-cos alpha+sin alpha}{-(-cos alpha+sin alpha)} =-1$