cos\alpha=\frac{3}{7}
sin^2+cos^2\alpha=1 jedynka trygonometryczna
sin^2\alpha+(\frac{3}{7})^2=1
sin^2\alpha+\frac{9}{49}=1
sin^2\alpha=1-\frac{9}{49}
sin^2\alpha=\frac{40}{49}
sin\alpha=\sqrt{\frac{40}{49}}=\frac{\sqrt{4\cdot 10}}{7}
sin\alpha=\frac{2\sqrt{10}}{7}
tg\alpha=\frac{sin\alpha}{cos\alpha}=\frac{\frac{2\sqrt{10}}{7}}{\frac{3}{7}}=\frac{2\sqrt{10}}{\not7^1}\cdot \frac{\not7^1}{3}=\frac{2\sqrt{10}}{3}
{sin^2\alpha-3tg^2 \alpha =(\frac{2\sqrt{10}}{7})^2- 3\cdot (\frac{2\sqrt{10}}{3})^2=\frac{4\cdot 10}{49}- \not3^1\cdot \frac{4\cdot 10}{\not9^3}=\frac{40}{49}- \frac{40}{3}=\frac{120-1960}{147}=-\frac{1840}{147}=-12\frac{76}{147}}