Find the Domain cos(2x)- square root of 2sin(x)=1

Problem

cos(2*x)−√(,2)*sin(x)=1

Solution

1. Identify the type of expression provided. The task asks for the domain of the equation cos(2*x)−√(,2)*sin(x)=1

2. Analyze the functions involved in the expression. The expression consists of a cosine function, cos(2*x) and a sine function, sin(x)

3. Determine the domain of the individual components. Both sin(x) and cos(x) are defined for all real numbers.

4. Check for restrictions. There are no denominators that could be zero, no logarithms of non-positive numbers, and no even-indexed roots containing variables (the square root is applied to the constant 2 not the variable x.

5. Conclude that since there are no values of x that make the expression undefined, the domain is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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