Use Fundamental Identities to Simplify the Expression Below and Then $\cos \alpha ( \sec \alpha - \cos \alpha )$

question 41

Multiple Choice

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

• A)​ \(\frac { \csc ^ { 2 } \alpha - \sec ^ { 2 } \alpha + \tan ^ { 2 } \alpha } { \csc ^ { 2 } \alpha }\)
• B)​ \(1 - \sin ^ { 2 } \alpha\)
• C)​ \(\frac { \csc ^ { 2 } \alpha - 1 } { \csc ^ { 2 } \alpha }\)
• D)​ \(1 - \cos ^ { 2 } \alpha\)
• E)​ \(1 - \cot ^ { 2 } \alpha\)

---

Definitions:

Satisfaction

The feeling of pleasure or fulfillment that comes from meeting one's needs or expectations.

Real Wages

Wages adjusted for inflation, reflecting the actual purchasing power of income.

Opportunity Cost

Opportunity cost represents the value of the best alternative that must be forgone as a result of choosing a particular action or decision over others.

Labor-saving Devices

Tools, machines, or systems that reduce the amount of labor needed to perform a task or produce a good.