Cosine and Sine addition and subtraction law with an automorphism

Youssef Aserrar, Elhoucien Elqorachi

Let $S$ be a semigroup. Our main results is that we describe the complex-valued solutions of the following functional equations \[g(xσ(y)) = g(x)g(y)+f(x)f(y),\ x,y\in S,\] \[f(xσ(…