Final answer:
The value of tan(arctan(2)) is 2 because arctan is the inverse function of tan, so applying arctan and then tan to a number returns the original number.
Step-by-step explanation:
The value of tan(arctan(2)) is 2. To see why, let's explore the definition of the arctan function, which is the inverse of the tan function. If you take the tan of an angle, and then calculate the arctan of that value, you end up back at the original angle. The arctan function answers the question: 'what angle has this tangent value?'. Since we started with tan(arctan(2)), essentially, we asked for the angle whose tangent is 2, and then immediately asked for the tangent of that angle, which brings us back to the original value of 2.