b)
[tex]ctg \alpha = 3 \ \ i \ \ ctg \alpha = \frac{cos\alpha}{sin\alpha} \\\\ \frac{cos\alpha}{sin\alpha} = 3 \ \ \ |\cdot sin\alpha \\ cos\alpha = 3sin\alpha \\\\ Zatem: \ \frac{8sin\alpha-cos\alpha}{7sin\alpha +6cos\alpha} =\frac{8sin\alpha-3sin\alpha}{7sin\alpha +6 \cdot 3sin\alpha} = \frac{5sin\alpha}{7sin\alpha +18sin\alpha} = \frac{5sin\alpha}{25sin\alpha} = \frac{5}{25} =\frac{1}{5}[/tex]
Odp. Wartość wyrażenia wynosi ¹/₅.
c)
[tex]tg \alpha = 4 \ \ i \ \ tg \alpha = \frac{sin\alpha}{cos\alpha} \\\\ \frac{sin\alpha}{cos\alpha} = 4 \ \ \ |\cdot cos\alpha \\ sin\alpha = 4cos\alpha \\\\ Zatem: \ \frac{cos\alpha+2sin\alpha}{sin\alpha -cos\alpha} =\frac{cos\alpha+2 \cdot 4cos\alpha}{4cos\alpha - cos\alpha} =\frac{cos\alpha+8cos\alpha}{3cos\alpha} =\frac{9cos\alpha}{3cos\alpha} =\frac{9}{3} =3[/tex]
Odp. Wartość wyrażenia wynosi 3.
