[tex]sin x = 0,75 =\frac{75}{100} = \frac{3}{4}[/tex]
Wiemy, że:
[tex]sn^{2}x + cos^{2}x = 1\\\\cos^{2}x = 1 - sin^{2}x = 1 - (\frac{3}{4})^{2} = \frac{16}{16}-\frac{9}{16} = \frac{7}{16}\\\\cos x = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{\sqrt{16}} = \frac{\sqrt{7}}{4}[/tex]
Więc:
[tex]2 - (cos x)^{2} = 2 - (\frac{\sqrt{7}}{4})^{2} =2-\frac{7}{16} = \frac{32}{16}-\frac{7}{16} = \frac{25}{16} = 1\frac{1}{16}[/tex]
