reserve x,x1,x2,x3 for Real;

theorem Th1:
  cos(x)<>0 implies cosec(x)=sec(x)/tan(x)
proof
  assume
A1: cos(x)<>0;
  then sec(x)/tan(x)=((1/cos(x))*cos(x))/((sin(x)/cos(x))*cos(x)) by
XCMPLX_1:91
    .=1/((sin(x)/cos(x))*cos(x)) by A1,XCMPLX_1:87
    .=1/sin(x) by A1,XCMPLX_1:87;
  hence thesis;
end;
