[latex] \sqrt{32} cos ^{2} \frac{13 \pi }{8} - \sqrt{32} sin ^{2} \frac{13 \pi }{8} [/latex] помогите решить, пожалуйста обьясните что откуда взято! 

[latex] \sqrt{32}cos^{2}\frac{13\pi}{8}-\sqrt{32}sin^{2}\frac{13\pi}{8}=\sqrt{32}(cos^{2}\frac{13\pi}{8}-sin^{2}\frac{13\pi}{8})= \\ =\sqrt{16*2}*cos(2*\frac{13\pi}{8})=4\sqrt{2}*cos\frac{13\pi}{4}=4\sqrt{2}*cos(\frac{8\pi}{4}+\frac{5\pi}{4})= \\ =4\sqrt{2}*cos(2\pi+\frac{5\pi}{4})=4\sqrt{2}*cos\frac{5\pi}{4}=4\sqrt{2}*cos(\frac{4\pi}{4}+\frac{\pi}{4})= \\ =4\sqrt{2}*cos(\pi+\frac{\pi}{4})=-4\sqrt{2}*cos\frac{\pi}{4}=-4\sqrt{2}*\frac{\sqrt2}{2}=-4[/latex]