
theorem Th5:
  for a being Real holds sin(a-PI) = -sin a & cos(a-PI) = - cos a
proof
  let r be Real;
  thus sin (r-PI) = sin(r)*cos(PI)-cos(r)*sin(PI) by Th3
    .= -sin r by SIN_COS:77;
  thus cos (r-PI) = cos(r)*cos(PI)+sin(r)*sin(PI) by Th3
    .= -cos r by SIN_COS:77;
end;
