Question

$2 { \cos }^{3} x - { \cos }^{2} + 2 \cos(x ) - 1 = 0$
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Answer 1

Ответ:

Объяснение:

Группировка

2cos^3(x) + 2cosx -cos^2(x) - 1 = 0

2cosx(cos^2(x) + 1)-1(cos^2x+1) = 0

(2cosx -1)(cos^2(x)+1) = 0 cos^2x +1 ≠0

Cosx=1/2

x = ±π/3 + 2πk, k є Z

Answer 2

$2Cos^{3}x-Cos^{2}x+2Cosx-1=0\\\\(2Cos^{3}x-Cos^{2}x)+(2Cosx-1)=0\\\\Cos^{2}x(2Cosx-1)+(2Cosx-1)=0\\\\(2Cosx-1)(Cos^{2} x+1)=0\\\\Cos^{2}x+1\neq0 \ ; \ \Rightarrow \ 2Cosx-1=0\\\\2Cosx=1\\\\Cosx=\frac{1}{2}\\\\x=\pm arc Cos\frac{1}{2}+2\pi n,n\in Z\\\\\boxed{x=\pm \frac{\pi }{3} +2\pi n, n\in Z}$