the sum of three consecutive positive numbers is 66. the smallest number is x. find the three numbers

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, $i \in \mathbb{N}_{O}$ .

<h3>How to solve a trigonometric equation</h3>

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, $i \in \mathbb{N}_{O}$

x₂ = 3π/4 ± 2π · i, $i \in \mathbb{N}_{O}$

x₃ = 5π/4 ± 2π · i, $i \in \mathbb{N}_{O}$

x₄ = 7π/4 ± 2π · i, $i \in \mathbb{N}_{O}$

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, $i \in \mathbb{N}_{O}$ .

To learn more on trigonometric equations: brainly.com/question/27821667

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