There are four solutions for the <em>trigonometric</em> 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, .
<h3>How to solve a trigonometric equation</h3>
In this problem we must simplify the <em>trigonometric</em> equation by both <em>algebraic</em> and <em>trigonometric</em> 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,
x₂ = 3π/4 ± 2π · i,
x₃ = 5π/4 ± 2π · i,
x₄ = 7π/4 ± 2π · i,
There are four solutions for the <em>trigonometric</em> 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, .
To learn more on trigonometric equations: brainly.com/question/27821667
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