Question

найдите значение выражения соs(
$alpha - beta$
если:
* фото *
​

Answer 1

$sinalpha cdot sinbeta =frac{1}{4}; ; ,; ; alpha +beta =frac{5pi }{4}$

$sinalpha cdot sinbeta =frac{1}{2}cdot Big (cos(alpha -beta )-cos(alpha +beta )Big )\\frac{1}{4}=frac{1}{2}cdot Big (cos(alpha -beta )-cosfrac{5pi }{4}Big )\\frac{1}{4}=frac{1}{2}cdot cos(alpha -beta )-frac{1}{2}cdot cos(pi +frac{pi}{4})\\frac{1}{4}=frac{1}{2}cdot cos(alpha -beta )-frac{1}{2}cdot (-cosfrac{pi}{4})\\frac{1}{4}=frac{1}{2}cdot cos(alpha -beta )+frac{1}{2}cdot frac{sqrt2}{2}\\frac{1}{2}cdot cos(alpha -beta )=frac{1}{4}-frac{sqrt2}{4}$

$cos(alpha -beta )=2cdot frac{1-sqrt2}{4}\\cos(alpha -beta )=frac{1-sqrt2}{2}$