reserve x, y, z, w for Real;
reserve n for Element of NAT;

theorem Th2:
  sinh x = 1/cosech x & cosh x = 1/sech x & tanh x = 1/coth x
proof
A1: sinh x = 1/(1/sinh x) by XCMPLX_1:56
    .= 1/cosech x by SIN_COS5:def 3;
A2: cosh x = 1/(1/cosh x) by XCMPLX_1:56
    .= 1/sech(x) by SIN_COS5:def 2;
  tanh x = sinh(x)/cosh(x) by Th1
    .= 1/(cosh(x)/sinh(x)) by XCMPLX_1:57
    .= 1/coth x by SIN_COS5:def 1;
  hence thesis by A1,A2;
end;
