Simplify tan(x+pi)

Problem

tan(x+π)

Solution

1. Identify the sum formula for the tangent function, which is tan(A+B)=(tan(A)+tan(B))/(1−tan(A)*tan(B))

2. Substitute A=x and B=π into the formula.

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

3. Evaluate the value of tan(π) Since sin(π)=0 and cos(π)=−1 it follows that 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

Final Answer

tan(x+π)=tan(x)

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