Question

sqrt(3)sinx+cosx=sqrt(2)

Answer 1

разделим на 2 каждый член уравнения

$frac{sqrt{3}}{2}sinx+frac{1}{2}cos x =frac{sqrt{2}}{2}$

$frac{sqrt{3}}{2}=cos{frac{pi}{6}}\ frac{1}{2}=sin{frac{pi}{6}}\ sin(x+frac{pi}{6})=frac{sqrt{2}}{2}\ x+frac{pi}{6} = frac{pi}{4}+2pi n\ x= -frac{pi}{6} + frac{pi}{4}+2pi n\ x = frac{pi}{12}+2pi n\ \ x+frac{pi}{6} = pi-frac{pi}{4}+2pi n\ x+frac{pi}{6} = frac{3pi}{4}+2pi n\ x=-frac{pi}{6} + frac{3pi}{4}+2pi n\ x = frac{7pi}{12}+2pi n$