Вычислите cos(45 - a) если cos a = -1\3, π\2< a< π

Решите задачу:

$\cos\left(45^o-\alpha\right)=\cos45^o\cos\alpha+\sin45^o\sin\alpha=\frac{\cos\alpha}{\sqrt2}+\frac{\sin\alpha}{\sqrt2}\\\cos\alpha=-\frac13\Rightarrow\sin\alpha=\sqrt{1-\cos^2\alpha}=\sqrt{1-\frac19}=\sqrt{\frac89}=\pm\frac{2\sqrt2}3\\\frac\pi2<\alpha<\pi\Rightarrow\sin\alpha=\frac{2\sqrt2}3\\\cos\left(45^o-\alpha\right)=-\frac1{2\sqrt2}+\frac{2\sqrt2}{3\sqrt2}=\frac{4\sqrt2-3}{6\sqrt2}$