Вычислить: 2) cos (a-П/4),если cos a=-1/3 П/2

[latex]cosa=-\frac{1}{3}\\\\\frac{\pi}{2}\ \textless \ a\ \textless \ \pi \quad \to \quad sina\ \textgreater \ 0\; ,\; \; sina=+\sqrt{1-cos^2a}\\\\sina=\sqrt{1-\frac{1}{9}}=\frac{\sqrt8}{3}=\frac{2\sqrt2}{3}\\\\cos(a-\frac{\pi}{4})=cosa\cdot cos\frac{\pi}{4}+sina\cdot sin\frac{\pi}{4}=\\\\=-\frac{1}{3}\cdot \frac{\sqrt2}{2}+\frac{2\sqrt2}{3}\cdot \frac{\sqrt2}{2}= \frac{-\sqrt2+4}{6} = \frac{\sqrt2\cdot (2\sqrt2-1)}{6} = \frac{2\sqrt2-1}{3\sqrt2} \approx 0,43[/latex]