Question

Срочно нужна помощь!!!

Answer 1

$sin^4( \frac{\pi}{8} )+cos^4(\frac{3\pi}{8})+sin^4(\frac{5\pi}{8})+cos^4(\frac{7\pi}{8})\\cos^4(\frac{7\pi}{8})=cos^4(\pi-\frac{\pi}{8})=(-cos(\frac{\pi}{8}))^4=cos^4(\frac{\pi}{8})$
Туже операцию проделываем и с sinx
$sin^4( \frac{5\pi}{8} )=sin^4(\pi- \frac{3\pi}{8} )=>sin^4(\frac{3\pi}{8})=sin^4(\pi-\frac{5\pi}{8} )\\sin^4(\frac{\pi}{8})+cos^4(\frac{\pi}{8})+sin^4(\frac{3\pi}{8})+cos^4( \frac{3\pi}{8} )=1-2sin^2(\frac{\pi}{8})cos^2(\frac{\pi}{8})+1-\\-2sin^2(\frac{3\pi}{8})cos^2(\frac{3\pi}{8})=1-\frac{1}{2}sin^2(\frac{\pi}{8}*2)+1-\frac{1}{2}sin^2(2*\frac{3\pi}{8})=\\=2-\frac{1}{2}(sin^2(\frac{\pi}{4})+sin^2(\frac{3\pi}{4}))=2-\frac{1}{2}(\frac{1}{2}+\frac{1}{2})=2-\frac{1}{2}=1,5$