Туже операцию проделываем и с sinx
sin^4(\frac{3\pi}{8})=sin^4(\pi-\frac{5\pi}{8} )\\sin^4(\frac{\pi}{8})+cos^4(\frac{\pi}{8})+sin^4(\frac{3\pi}{8})+cos^4( \frac{3\pi}{8} )=1-2sin^2(\frac{\pi}{8})cos^2(\frac{\pi}{8})+1-\\-2sin^2(\frac{3\pi}{8})cos^2(\frac{3\pi}{8})=1-\frac{1}{2}sin^2(\frac{\pi}{8}*2)+1-\frac{1}{2}sin^2(2*\frac{3\pi}{8})=\\=2-\frac{1}{2}(sin^2(\frac{\pi}{4})+sin^2(\frac{3\pi}{4}))=2-\frac{1}{2}(\frac{1}{2}+\frac{1}{2})=2-\frac{1}{2}=1,5" alt="sin^4( \frac{5\pi}{8} )=sin^4(\pi- \frac{3\pi}{8} )=>sin^4(\frac{3\pi}{8})=sin^4(\pi-\frac{5\pi}{8} )\\sin^4(\frac{\pi}{8})+cos^4(\frac{\pi}{8})+sin^4(\frac{3\pi}{8})+cos^4( \frac{3\pi}{8} )=1-2sin^2(\frac{\pi}{8})cos^2(\frac{\pi}{8})+1-\\-2sin^2(\frac{3\pi}{8})cos^2(\frac{3\pi}{8})=1-\frac{1}{2}sin^2(\frac{\pi}{8}*2)+1-\frac{1}{2}sin^2(2*\frac{3\pi}{8})=\\=2-\frac{1}{2}(sin^2(\frac{\pi}{4})+sin^2(\frac{3\pi}{4}))=2-\frac{1}{2}(\frac{1}{2}+\frac{1}{2})=2-\frac{1}{2}=1,5" align="absmiddle" class="latex-formula">