I summarize all identities into general expression sum(((2*n)!*(2*cosh(x)+2*cos(t))^(-n-1/2)*(abs(sin(t)))^(2*n+1)*cosh((n+1/2)*x))/((2*n+1)*2^(2*n)*n!^2),n=0..inf)=t/2;t in ]-Pi/2, Pi/2[ sum(((2*n)!*(2*cosh(x)+2*cos(t))^(-n-1/2)*(sin(t))^(2*n+1)*sinh((n+1/2)*x))/((2*n+1)*2^(2*n)*n!^2),n=0..inf)=Pi/2-t/2; t in ]Pi/2, 0[U]0 , 3*Pi/2[ Best regards