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:

Osler Nodes

Red, painful, elevated sores on the hands and feet linked to infectious endocarditis.

Janeway Spots

Small, painless, red or purple spots on the palms or soles, associated with infective endocarditis.

Analgesics

Medications designed specifically to relieve pain without causing the loss of consciousness.

Rheumatic Fever

An inflammatory disease that can develop after a Group A Streptococcus bacterial infection, potentially damaging heart valves and other tissues.