sin (60 + 45) + cos (60 + 45) = do you remember angle sum trig identities?
Sin (A+B) = SInA CosB + sinB Cos A
and
Cos(A+B) = cos A Cos B - Sin A Sin B
So the first 1/2 would be
sqrt3/2 * sqrt2/2 + sqrt2/2 * 1/2
to this you would add the Cos (A+B) part