Use the sum-to-product formulas to select the sum or difference as a product. $$\cos ( 5 \phi + 2 \pi ) + \cos 5 \phi$$
A) $- 2 \cos 5 \phi \cos \pi$
B) $- 2 \cos 5 \pi$
C) $2 \cos ( 5 \phi + \pi ) \cos \pi$
D) $2 \cos ( \phi + \pi ) \cos \pi$
E) $2 \cos ( 5 \phi + \pi )$

Question

Use the sum-to-product formulas to select the sum or difference as a product.​ $$\cos ( 5 \phi + 2 \pi ) + \cos 5 \phi$$ ​
A)​ $- 2 \cos 5 \phi \cos \pi$
B)​ $- 2 \cos 5 \pi$
C) $2 \cos ( 5 \phi + \pi ) \cos \pi$
D)​ $2 \cos ( \phi + \pi ) \cos \pi$
E)​ $2 \cos ( 5 \phi + \pi )$

Quizplus · Accepted Answer

Using the sum-to-product formula, $$\cos ( 5 \phi + 2 \pi ) + \cos 5 \phi = 2 \cos \left( \frac{5 \phi + 2 \pi + 5 \phi}{2} \right) \cos \left( \frac{5 \phi + 2 \pi - 5 \phi}{2} \right)$$$$= 2 \cos ( 5 \phi + \pi ) \cos \pi$$

Use the Sum-To-Product Formulas to Select the Sum or Difference cos⁡(5ϕ+2π)+cos⁡5ϕ\cos ( 5 \phi + 2 \pi ) + \cos 5 \phicos(5ϕ+2π)+cos5ϕ

Use the Sum-To-Product Formulas to Select the Sum or Difference $\cos ( 5 \phi + 2 \pi ) + \cos 5 \phi$