Find the Exact Value of the Expression, If Possible $\cos \left( \tan ^ { - 1 } x \right)$

question 96

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\cos \left( \tan ^ { - 1 } x \right)$

• A) \(\frac { \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)
• B) \(\frac { \sqrt { x ^ { 2 } - 1 } } { x ^ { 2 } - 1 }\)
• C) \(x \sqrt { x ^ { 2 } + 1 }\)
• D) \(\frac { x \sqrt { x ^ { 2 } + 1 } } { x ^ { 2 } + 1 }\)

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Definitions:

Materialism

An orientation emphasizing possessions and money for personal happiness and social progress.

Doctrine Of Natural Liberty

A philosophical belief emphasizing that individuals have the right to live their lives with minimal governmental interference, advocating for freedom in personal and economic matters.

Economic Self-interest

The concept that individuals will make decisions based on the pursuit of their own financial gain or well-being.

Ethical Concept

Involves the principles and values that guide the behavior of individuals or groups regarding what is right and wrong, impacting decisions and actions.