Find the Domain cos(2x)+0.5=cos(x)

Problem

cos(2*x)+0.5=cos(x)

Solution

1. Identify the type of expression provided. The expression cos(2*x)+0.5=cos(x) is a trigonometric equation.

2. Determine the functions involved. The equation consists of cosine functions, specifically cos(2*x) and cos(x) and a constant 0.5

3. Recall the domain of the cosine function. The function cos(θ) is defined for all real numbers θ

4. Analyze the arguments. The arguments 2*x and x are linear polynomials, which are defined for all real numbers x

5. Conclude the domain. Since there are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers, the equation is defined for all real values of x

Final Answer

Domain: *(−∞,∞)

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