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Given the original text's complexity and apparent confusion, here is a coherent and properly formatted mathematical question:

Solve for [tex]\( x \)[/tex]:
[tex]\[ \cos(3x + 2) = \cos\left(x + \frac{11}{3}\right) \][/tex]

Sagot :

GinnyAnswer
To solve this mathematical expression, we need to first analyze the components thoroughly.

1. Identify the problematic part: The "Mesoudre equation" part does not provide a clear mathematical expression, making it ambiguous.
2. Simplified problem: Let's assume we're focusing on the computable part of the expression [tex]$\operatorname{Cos}(3x + 2 - \cos \left(x + \frac{11}{3}\right))$[/tex].

However, without further clarification on "Mesoudre equation" and as it stands, we cannot perform any further step-by-step calculations due to the incomplete information. Consequently, the result remains indeterminate as one crucial part of the equation lacks definition.

Hence, the value of the given expression is

[tex]\[ \text {None} \][/tex]

This highlights the need for a complete and clear mathematical problem statement for accurate computation.
sqdancefan

Answer:

  For any integer k, ...

  • x = 5/6 + kπ
  • x = -17/12 + kπ/2

Step-by-step explanation:

You want the solutions to the equation cos(3x+2) = cos(x+11/3).

Cosine

The cosine function is an even function with period 2π. This means ...

  cos(x) = cos(2kπ±x)

Using this to find the solutions of the given equation, we have ...

  cos(3x+2) = cos(2kπ ± (x +11/3))

Function values are the same when the arguments are the same:

  3x +2 = 2kπ ± (x + 11/3)

Two equations

This resolves to two equations.

  [tex]3x+2=2k\pi+x+\dfrac{11}{3}\\\\9x+6=6k\pi+3x+11\qquad\text{multiply by 3}\\\\6x=6k\pi+5\qquad\text{subtract $3x+6$}\\\\\boxed{x=\dfrac{5}{6}+k\pi}\qquad\text{divide by 6}[/tex]

And the other equation is ...

  [tex]3x+2=2k\pi-x-\dfrac{11}{3}\\\\9x+6=6k\pi-3x-11\qquad\text{multiply by 3}\\\\12x=6k\pi-17\qquad\text{add $3x-6$}\\\\\boxed{x=\dfrac{k\pi}{2}-\dfrac{17}{12}}\qquad\text{divide by 12}[/tex]

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