Question

Упростите выражение и найдите его значение:
sin(a+b)-2 cosasinß/2sinasinß+cos(a+b)'
если а — b= 135°​

Answer 1

Объяснение:

$\alpha -\beta =135^0\\\frac{sin(\alpha +\beta )-2*cos\alpha *sin\beta }{2*sin\alpha *sin\beta +cos(\alpha +\beta )} =\frac{sin(\alpha +\beta )-2*\frac{1}{2}*(sin(\alpha +\beta )-sim(\alpha -\beta )) }{2*\frac{1}{2}*(cos(\alpha -\beta )-cos(\alpha +\beta )) +cos(\alpha +\beta )}=\\=\frac{sin(\alpha +\beta )-sin(\alpha +\beta )+sin(\alpha -\beta )}{cos(\alpha -\beta) -cos(\alpha +\beta )+cos(\alpha +\beta )}=\frac{sin(\alpha -\beta )}{cos(\alpha -\beta )}=tg(\alpha -\beta )=tg135^0=-1.$