Hello, It seems that this identity is correct for all t in] -Pi / 2; Pi / 2 [ Someone would have any idea?? Pi/8=sum(((-1)^n*(sqrt(cos(t)^2+1)-cos(t))^(2*n+1)*cos((2*n+1)*t))/(2*n+1),n=0..infinity) ; Already known?? What are the references? thank you FME...