Z zalozen wiemy ze
[tex]tg\alpha = \frac75\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\\frac{sin\alpha}{cos\alpha} = \frac75 /*cos\alpha\\sin\alpha = \frac75cos\alpha[/tex]
Dla ulatwienia zapisu upraszczamy osobno licznik i mianownik.
[tex]sin\alpha cos\alpha = \frac{7}{5}cos\alpha * cos\alpha = \frac{7}{5} cos^2\alpha\\cos^2\alpha - sin^2\alpha = cos^2\alpha - (\frac75cos\alpha)^2=cos^2\alpha-\frac{49}{25}cos^2\alpha = \frac{25}{25}cos^2\alpha-\frac{49}{25}cos^2\alpha=-\frac{24}{25}cos^2\alpha[/tex]
I rozwiazujemy nasze wyrazenie[tex]\frac{sin\alpha cos\alpha}{cos^2\alpha - sin^2\alpha} = \frac{\frac75cos^2\alpha}{-\frac{24}{25}cos^2\alpha} = \frac{\frac{7}{5}}{-\frac{24}{25}} = \frac{7}{5} * \frac{1}{-\frac{24}{25}} = \frac75*(1:(-\frac{24}{25}))=\frac75*(1*(-\frac{25}{24})) = \frac75*(-\frac{25}{24}) = -\frac{7*5}{24} = -\frac{35}{24} = -1\frac{11}{24}[/tex]
