reserve th, th1, th2, th3 for Real;

theorem Th5:
  cos(th)*cos(th) = 1-sin(th)*sin(th)
proof
  cos(th)*cos(th) = cos(th)*cos(th)+(1-1)
    .= cos(th)*cos(th)+(1---(sin(th)*sin(th)+cos(th)*cos(th))) by SIN_COS:29
    .= 1-sin(th)*sin(th);
  hence thesis;
end;
