Simplify tan(pi/4-x)

Problem

tan(π/4−x)

Solution

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

2. Substitute the values A=π/4 and B=x into the formula.

tan(π/4−x)=(tan(π/4)−tan(x))/(1+tan(π/4)*tan(x))

3. Evaluate the specific value tan(π/4)=1

tan(π/4−x)=(1−tan(x))/(1+(1)*tan(x))

4. Simplify the expression by performing the multiplication in the denominator.

tan(π/4−x)=(1−tan(x))/(1+tan(x))

Final Answer

tan(π/4−x)=(1−tan(x))/(1+tan(x))

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