use sin(x-3)= sin(x)cos(3)-cos(x)sin(3).

then f(x) takes the form p(sinx) + q(cosx).

its maximum value is sqrt(p^2+q^2).

to see this let sqrt(p^2+q^2)=k

then f(x)=p(sinx)+q(cosx)= k[(p/k)(sinx)+ (q/k)(cosx)].

observe that p/k can be taken as cos of some angle say 'y' so p/k=cosy.

this forces q/k=siny.

f(x)= k[(cosy)(sinx)+(siny)(cosx)]= k(sin(x+y)). clearly its maximum is k.