Final answer:
The question seems to contain a typo as the values provided are not angle measures. To find tan(a-b) and tan(a+b), the tangent values for specific angles must be known, and using the tangent addition and subtraction formulas are then applied.
Step-by-step explanation:
To find the exact values of tan(a-b) and tan(a+b) with given values a=3/4 and b=-8, we should use the tangent addition and subtraction formulas:
- tan(a-b) = \( \frac{tan(a) - tan(b)}{1 + tan(a)tan(b)} \)
- tan(a+b) = \( \frac{tan(a) + tan(b)}{1 - tan(a)tan(b)} \)
Since the values of a and b are given as numbers, not angles, we cannot proceed directly to find tan(a-b) and tan(a+b) as they stand. Instead, we should either know or calculate the tangent values for 3/4 and -8, which usually are not defined for non-angle numbers.
Assuming there is a typo and that correct angle measures were meant to be provided, we'd compute the tangent of the angles (in radians or degrees) and then substitute into the formulas. Without the correct angle measures or more context, finding an exact value or simplifying further is not possible.