Find the Exact Value tan(arctan(pi))

Problem

tan(arctan(π))

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 ƒ*(ƒ(x)(−1))=x for all x in the domain of the inverse function.

3. Determine the domain of the arctangent function, which is the set of all real numbers (−∞,∞)

4. Verify that π is a real number, which means it falls within the domain of the arctangent function.

5. Simplify the expression using the identity tan(arctan(x))=x

Final Answer

tan(arctan(π))=π

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