a) \(\dfrac{{1 - tg\alpha }}{ {1 + tg\alpha }} = \dfrac{{1 - \dfrac{{\sin \alpha }}{{{\rm{cos}}\alpha }}}}{{1 + \dfrac{{\sin \alpha }}{{{\rm{cos}}\alpha }}}} \)\(= \dfrac{{{\rm{cos}}\alpha - \sin \alpha }}{{{\rm{cos}}\alpha + \sin \alpha }}.\)
b) \(\dfrac{{{\rm{cos}}\alpha - \sin \alpha }}{{{\rm{cos}}\alpha + \sin \alpha }}\)\(= \dfrac{{\dfrac{{\cos \alpha }}{{\cos \alpha }} - \dfrac{{\sin \alpha }}{{\cos \alpha }}}}{{\dfrac{{\cos \alpha }}{{\cos \alpha }} + \dfrac{{\sin \alpha }}{{\cos \alpha }}}}\)\( = \dfrac{{1 - tg\alpha }}{{1 + tg\alpha }} = \dfrac{{1 - \dfrac{1}{3}}}{{1 + \dfrac{1}{3}}} = \dfrac{1}{2}.\)
