Question

Система: cosx * cosy = 1/6 tgx * tgy = 2 Найти: cos (x+y) = ?

Answer 1

cos(x+y)=cosx*cosy-sinx*siny

 

tgx*tgy=2

$frac{sinx}{cosx}*frac{siny}{cosy}=2$

$frac{sinx*siny}{cosx*cosy}=2$

$frac{sinx*siny}{frac{1}{6}}=2$

sinx*siny=2*$frac{1}{6}$

sinx*siny=$frac{2}{6}$

cos(x+y)=cosx*cosy-sinx*siny=$frac{1}{6}$-$frac{1}{3}$=$frac{1-2}{6}$=$frac{-1}{6}$