Final answer:
The exact value of tan(-π/12) is -2 + sqrt(3).
Step-by-step explanation:
To find the exact value of tan(-π/12), we can use the subtraction formula for tangent: tan(x - y) = (tan(x) - tan(y))/(1 + tan(x)*tan(y)).
In this case, x = 0 and y = π/12. So, tan(-π/12) = (tan(0) - tan(π/12))/(1 + tan(0)*tan(π/12)).
tan(0) is 0 and tan(π/12) is 2 - sqrt(3). Substituting these values into the formula, we get (0 - (2 - sqrt(3)))/(1 + 0*(2 - sqrt(3))).
Finally, evaluating the expression, we get -2 + sqrt(3) as the exact value of tan(-π/12).