Use a Product-To-Sum Formula to Convert the Expression to a Sum

question 17

Multiple Choice

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos \frac { \pi } { 5 } \cos \frac { 4 \pi } { 5 }$

• A) \(\frac { 1 } { 2 } \left( \cos \frac { 3 \pi } { 5 } + 1 \right)\)
• B) \(\frac { 1 } { 2 } \left( \cos \frac { 3 \pi } { 5 } - 1 \right)\)
• C) \(1 + \sin ^ { 2 } \frac { \pi } { 5 }\)
• D) \(- \frac { 1 } { 2 } \sin \frac { 3 \pi } { 5 }\)
• E) \(1 - \sin ^ { 2 } \frac { \pi } { 5 }\)

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Definitions:

Excess Capacity

A situation in which a firm produces less than the maximum output due to lack of demand or strategic choice, leading to underutilized resources.

Average Total Cost

The total cost of production (fixed plus variable costs) divided by the number of units produced, representing the cost per unit.

Monopolistically Competitive

A market structure where many firms sell products that are similar but not identical, allowing for competition based on quality, price, and brand.

Long-Run Equilibriums

A state in a market where all firms are making zero economic profit, and no new firms enter or exit the industry, resulting in a stable market condition over time.