theorem Th41:
  tan.0 = 0 & tan 0 =0
proof
A1: 0 in ].-PI/2,PI/2.[ by XXREAL_1:4;
  then tan.0 = 0/cos.0 by Th1,RFUNCT_1:def 1,SIN_COS:30
    .= 0;
  hence thesis by A1,Th13;
end;
