Question

Помогите решить 2cos^2+cosx=0

Answer 1

2cos²x+cosx=0
cosx(2cosx+1)=0
1) cosx=0
    x=π/2 +πn, n∈Z

2) 2cosx+1=0
2cosx=-1
cosx=-1/2
x=+ (2π/3) +2πn, n∈Z

Ответ: х=π/2 +πn, n∈Z.
           x=+ (2π/3) +2πn, n∈Z.

Answer 2

$2cos ^{2} x+cosx=0\\cosx(2cosx+1)=0\\cosx=0\\x= \frac{ \pi }{2} + \pi n\\\\cosx=- \frac{1}{2} \\x=+-( \pi - \frac{ \pi }{3} )+2 \pi k\\x=+- \frac{2 \pi }{ 3} +2 \pi k$

n,k  ∈ Z