Question

Упростите выражение.
Даю 25 баллов

Answer 1

(cos(45+b)+sin(45+b))/(cos(45+b)-sin(45+b))

=√2*sin(45+45+b)/(√2*sin(45-45-b)=

sin(90+b)/sin(-b)=
cosb/(-sinb)=-ctgb

Answer 2

$=\frac{Sin(90-(45+\beta))+Sin(45+\beta)}{Sin(90-(45+\beta))-Sin(45+\beta)}=\frac{Sin(45-\beta)+Sin(45+\beta)}{Sin(45-\beta)-Sin(45+\beta)}=\frac{2Sin\frac{45-\beta+45+\beta }{2}*Cos\frac{45-\beta-45-\beta}{2}}{2Sin\frac{45-\beta-45-\beta  }{2} *Cos\frac{45-\beta+45+\beta}{2}} =\frac{Sin45*Cos\beta }{Sin\beta*Cos45 }=\frac{\sqrt{2} *Cos\beta }{Sin\beta*\sqrt{2}}=\frac{Cos\beta }{Sin\beta }=Ctg\beta$