Simplify tan(pi-x)

Problem

tan(π−x)

Solution

1. Identify the trigonometric identity for the tangent of a difference of two angles.

2. Apply the formula tan(A−B)=(tan(A)−tan(B))/(1+tan(A)*tan(B)) where A=π and B=x

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

3. Evaluate the value of tan(π) Since sin(π)=0 and cos(π)=−1 we have tan(π)=0

tan(π)=0

4. Substitute the value of tan(π) back into the expression.

tan(π−x)=(0−tan(x))/(1+(0)*tan(x))

5. Simplify the resulting fraction.

tan(π−x)=(−tan(x))/1

tan(π−x)=−tan(x)

Final Answer

tan(π−x)=−tan(x)

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