Question

Find the exact value of the expression tan(arctan(5)).

Answer 1

The exact value of the expression tan(arctan(5)) is 5.

Step-by-step explanation:

To find the exact value of the expression tan(arctan(5)), we can use the fact that the tangent function and the inverse tangent function are inverses of each other. Since arctan(5) gives us an angle whose tangent is 5, we can say that tan(arctan(5)) = 5.

Answer 2

The exact value of tan(arctan(5)) is 5 because the arctan function and the tangent function are inverse operations.

Step-by-step explanation:

A problem that involves the composition of a trigonometric function and its inverse. The problem tan(arctan(5)) directly asks for the tangent of the arctan of 5.

When you take the arctan (or inverse tangent) of a number, you are finding the angle whose tangent is that number. Then, when you take the tangent of this angle, you are essentially undoing the arctan. Therefore, the answer for tan(arctan(5)) is simply 5.