Geometry

Question Analysis

The main focus of this problem is to evaluate the composition of a trigonometric function () and an inverse trigonometric function (). We first need to find the angle whose cosine is using the inverse cosine function and then find the tangent of that angle. Since the domain of the inverse cosine function is and , and the range of 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. Once we find the angle from , we use the tangent function to find the value of . In a right triangle, the tangent function for an angle is defined as . We can also use the identity after finding the angle .

 

Step - by - Step Solution

1. First, find the value of :

We know that and is in the range . So,

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