Verify the Identity tan(x-pi)=tan(x)

Problem

tan(x−π)=tan(x)

Solution

1. Identify the tangent subtraction identity, which states that for any angles a and b

tan(a−b)=(tan(a)−tan(b))/(1+tan(a)*tan(b))

2. Substitute the values a=x and b=π into the identity:

tan(x−π)=(tan(x)−tan(π))/(1+tan(x)*tan(π))

3. Evaluate the tangent of π using the unit circle or trigonometric properties:

tan(π)=0

4. Simplify the expression by replacing tan(π) with 0

tan(x−π)=(tan(x)−0)/(1+tan(x)⋅0)

5. Reduce the fraction to its simplest form:

tan(x−π)=tan(x)/1

6. Conclude that the left side equals the right side:

tan(x−π)=tan(x)

Final Answer

tan(x−π)=tan(x)

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