Cos(45*-a)-sin(a+45)=

$cos(45^o-a)-sin(a+45^o)$

Воспользуемся формулой: $sina-cosb=2sin(\frac{a+b}2-\frac{\pi}4)*cos(\frac{a-b}2+\frac{\pi}4)$

$-(sin(a+45^o)-cos(45^o-a))=-2sin(\frac{a+45^o+45^o-a}2-\frac{\pi}4)*\\ *cos(\frac{a+45^o-45^o+a}2+\frac{\pi}4)=-2sin(45^o-\frac{\pi}4)*cos(a+\frac{\pi}4)=\\=-2sin(\frac{\pi}4-\frac{\pi}4)*cos(a+\frac{\pi}4)=-2sin0*cos(a+\frac{\pi}4)=0$

Ответ: 0.