[tex]\alpha ~~-kat~~ostry\\\\korzystam~~ze~~wzorow:\\\\tg\alpha =\dfrac{sin\alpha }{cos\alpha } ,~~ctg\alpha =\dfrac{cos\alpha }{sin\alpha} ~~oraz~~sin^{2} \alpha +cos^{2} \alpha =1\\\\Wykazac:~~sin\alpha\cdot \cos\alpha =\dfrac{1}{3} \\\\tg\alpha +ctg\alpha =3\\\\\dfrac{sin\alpha }{cos\alpha } +\dfrac{cos\alpha }{sin\alpha } =3\\\\\dfrac{sin\alpha \cdot sin\alpha +cos\alpha \cdot cos\alpha }{sin\alpha \cdot cos\alpha } =3\\\\[/tex]
[tex]\dfrac{sin^{2} \alpha +cos^{2} \alpha }{sin\alpha \cdot cos\alpha } =3\\\\\dfrac{1}{sin\alpha \cdot cos\alpha } =3\\\\\dfrac{1}{sin\alpha \cdot cos\alpha } =\dfrac{3}{1} \\\\3\cdot sin\alpha \cdot cos\alpha=1\cdot 1~~\mid \div 3\\\\sin\alpha \cdot cos\alpha=\dfrac{1}{3} ~~~~cbdu[/tex]
