Final answer:
To express tan 105 degrees in terms of the tangent of a positive acute angle, we can subtract 180 degrees from 105 degrees to find an equivalent angle that is within the range of 0 to 90 degrees. So, tan 105 degrees is equal to tan (-75 degrees).
Step-by-step explanation:
To express tan 105 degrees in terms of the tangent of a positive acute angle, we need to find a positive acute angle whose tangent is equal to the tangent of 105 degrees. Since the tangent function has a period of 180 degrees, we can subtract 180 degrees from 105 degrees to find an equivalent angle that is within the range of 0 to 90 degrees. 105 - 180 = -75 degrees. So, we have tan 105 degrees = tan (-75 degrees). Therefore, the correct answer is option A: tan(105°) = -tan(75°).