Find the Exact Value tan(pi/4-2)

Problem

tan(π/4−2)

Solution

1. Identify the appropriate trigonometric identity for the tangent of a difference, which is tan(A−B)=(tan(A)−tan(B))/(1+tan(A)*tan(B))

2. Assign the values from the expression to the variables in the identity, where A=π/4 and B=2

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

4. Substitute these values into the difference formula to get (1−tan(2))/(1+(1)*tan(2))

5. Simplify the resulting expression to its final form.

Final Answer

tan(π/4−2)=(1−tan(2))/(1+tan(2))

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