## Mellin transform

Can someone give me some help on this problem?
Show that $\mu(cos)(z)=\int_0^{\infty}cos(t)t^{z-1}dt=\Gamma(z)cos(\pi z/2)$ for $0.
By definition, $\mu(f)(z)=F(z)=\int_0^{\infty}f(t)t^{z-1}dt$
If I know that $\mu(sin)(z)=\int_0^{\infty}sin(t)t^{z-1}dt=\Gamma(z)sin(\pi z/2)$ for $0, how can I show that this identity still holds in the larger strip $-1