# How do you use the product to sum formulas to write 5cos(-5beta)cos3beta as a sum or difference?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Feb 17, 2017

See below

#### Explanation:

Firstly, the sum of cosines is always written in the form $2 \cos \left(\frac{\text{P"+"Q")/2)cos(("P"-"Q}}{2}\right)$, so we have to take the $5$ out.

$5 \cos \left(- 5 \beta\right) \cos 3 \beta = \frac{5}{2} \left(2 \cos \left(- 5 \beta\right) \cos 3 \beta\right)$

Since $\cos x$ is an even function, we know that $\cos \left(- 5 \beta\right) = \cos \left(5 \beta\right)$

$\frac{5}{2} \left(2 \cos \left(- 5 \beta\right) \left(3 \beta\right)\right) = \frac{5}{2} \left(2 \cos 5 \beta \cos 3 \beta\right)$

Now it is trivial to find $\text{P}$ and $\text{Q}$

$\text{P} = 5 \beta + 3 \beta = 8 \beta$

$\text{Q} = 5 \beta - 3 \beta = 2 \beta$

$\frac{5}{2} \left(2 \cos 5 \beta \cos 3 \beta\right) = \frac{5}{2} \left(\cos 8 \beta + \cos 3 \beta\right)$

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer
• 15 minutes ago
• 22 minutes ago
• 26 minutes ago
• 31 minutes ago
• 43 seconds ago
• 5 minutes ago
• 8 minutes ago
• 9 minutes ago
• 11 minutes ago
• 11 minutes ago
• 15 minutes ago
• 22 minutes ago
• 26 minutes ago
• 31 minutes ago
• Che
• Cal
• Pre
• Bio
• Phy
• Alg
• Tri
• Sta
• Ear
• Org
• Geo
• Wor
• Psy
• Ana
• Ast
• Ast
• U.S
• Eng
• Pre
• Env
• Soc