The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation     f₁(xy)+f₂(xσ(y))=2g₁(x)g₂(y),  x,y∈G,   where G is an arbitrary group, f₁,f₂,g₁ and g₂ are complex valued functions on G and σ is an involution of G. Results of this paper also can be extended to the setting of monoids (that is, a semigroup with identity) that need not be abelian.