The main focus of this paper is to give some coefficient estimates for the analytic and univalent functions on the open unit disk in the complex plane that are subordinated to cosine and sine functions with complex order. For the defined three subclasses of analytic and univalent functions S*(s_cos,sin ∈ C_cos,sin)(τ, β), τ ∈ C − {0} and β ∈ [0,1], satisfying a certain subordination condition to cos z + sin z, we obtain the coefficient estimates for the initial two coefficients and examine the Fekete-Szego problem for the mentioned class.