Question

Решительно уравнение
2sin^2)x+3cos x - 3=0

Answer 1

$2(1-cos^{2}x)+3cosx-3=0 \y=cosx \2-2y^{2}+3y-3=0 \-2y^{2}+3y-1=0 \2y^{2}-3y+1=0 \D=(-3)^{2}-4*2*1=9-8=1 \y_{1}= frac{3+1}{4} =1 \y_{2}=frac{3-1}{4} =frac{1}{2} \cosx=1 \x=0+2pi n=2pi n \cosx= frac{1}{2} \x_{1}=frac{pi}{3} +2pi n \x_{2}=-frac{pi}{3} +2pi n$
Ответ: $x_{1}=2pi n; x_{2}=frac{pi}{3}+2pi n; x3=-frac{pi}{3}+2pi n$