There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].
How to solve a trigonometric equation
In this problem we must simplify the trigonometric equation by both algebraic and trigonometric means and clear the variable x:
2 · cos x = 4 · cos x · sin² x
2 · sin² x = 1
sin² x = 1/2
sin x = ± √2 /2
There are several solutions:
x₁ = π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]
x₂ = 3π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]
x₃ = 5π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]
x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]
There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].
To learn more on trigonometric equations: https://brainly.com/question/27821667
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