Simplify tan(2pi-x)

Problem

tan(2*π−x)

Solution

1. Identify the periodicity of the tangent function. The tangent function has a period of π which means tan(θ+n*π)=tan(θ) for any integer n

2. Apply the periodicity property by recognizing that 2*π is a multiple of the period.

tan(2*π−x)=tan(−x)

3. Use the odd-even identity for the tangent function, which states that tan(−θ)=−tan(θ)

tan(−x)=−tan(x)

Final Answer

tan(2*π−x)=−tan(x)

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