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In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f\left(x\sigma \right(y\left)a\right)+f\left(xya\right)=2f\left(x\right)f\left(y\right)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f\left(x\sigma \right(y\left)a\right)-f\left(xya\right)=2f\left(x\right)f\left(y\right),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.