Find the Exact Value tan(arctan(5))

Problem

tan(arctan(5))

Solution

1. Identify the relationship between the tangent function and its inverse, the arctangent function.

2. Apply the property of inverse functions, which states that for any value x in the domain of the inverse function, tan(arctan(x))=x

3. Determine if the value x=5 is within the domain of the arctangent function. Since the domain of arctan(x) is all real numbers (−∞,∞) the property applies directly.

4. Evaluate the expression by simplifying the composition of the function and its inverse.

Final Answer

tan(arctan(5))=5

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