Step-by-step-explanation:
Step 1: Start with the expression tan(π - θ).
Step 2: Use the fact that the tangent function has a period of π, meaning the value of the tangent function repeats every π radians. This means that tan(π - θ) is equivalent to tan(-θ), because adding π to an angle does not change the value of the tangent function.
Step 3: Then, recall that the tangent function is an odd function, which means tan(-θ) = -tan(θ) for any angle θ. This is a fundamental property of the tangent function.
Step 4: Combining the previous steps, we have:
tan(π - θ) = tan(-θ) (from step 2)
tan(-θ) = -tan(θ) (from step 3)
Therefore, we conclude that:
tan(π - θ) = -tan(θ).
By following these steps, we have shown step by step that the given identity, tan(π - θ) = -tan(θ), is indeed true.
