[math-fun] Identities for Pi (04)

to finish Pi/12=sum((1/(2*n+1))*(-sqrt(3)*sin(x)+sqrt(3*(sin(x))^2+1))^(2*n+1)*sin((2*n+1)*x),n=0..infinity); Pi/12=sum(((-1)^n/(2*n+1))*(sqrt(3)*sinh(x)-sqrt(3*(sinh(x))^2-1))^(2*n+1)*sinh((2*n+1)*x),n=0..infinity); (1/12)*Pi = sum((-1)^n/(2*n+1)*(-sqrt(3)*cosh(x)+(3*cosh(x)^2+1)^(1/2))^(2*n+1)*cosh((2*n+1)*x),n = 0 .. infinity); (1/6)*Pi = sum((-1)^n/(2*n+1)*(-(1/sqrt(3))*cosh(x)+((1/3)*cosh(x)^2+1)^(1/2))^(2*n+1)*cosh((2*n+1)*x),n = 0 .. infinity); With a general formula arctan(t) = f(t,x)