Geometry

Question Analysis

The main focus of this problem is to evaluate the composition of the tangent function and the inverse cosine function. We need to first find the angle whose cosine is using the inverse cosine function , and then determine the tangent of that angle. Given that the domain of is and , and its range is , we will work within this range to solve the problem.

 

Key Concept Explanation

1. The inverse cosine function, or , gives the angle such that and .

2. To find for the angle obtained from , we can use the right triangle relationships. If , we can find the opposite side using the Pythagorean theorem (where is the hypotenuse and and are the legs of the right triangle), and then .

 

Step - by - Step Solution

1. Let , so .

Assume a right triangle where the adjacent side to the angle is and the hypotenuse is

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