Assistance please!

Question

Rewrite 3[cos(5x)+cos(3x)] as the product of sine and/or cosine functions.

Answer 1

Hi Bailey!

Try using the formula

cos(α)cos(β) = 1⁄2 [ cos(α+β) + cos(α-β) ]

To see how it can fit your question multiply the above identity by 6 to get

6cos(α)cos(β) = 6(1⁄2 [ cos(α+β) + cos(α-β) ] ) = 3 [ cos(α+β) + cos(α-β) ]

Then just set α+β = 5 and α-β =3

which gives α = 4 and β = 1

Thus,

6cos(4x)cos(x) = 3 [ cos(5x) + cos(3x) ]

Answer 2

You are told to write this as the product of sin or cos functions. You can either take the hint and eventually figure it out, look for the formula in your book that relates sums to products, or do a web search on sums of cosines as product

Web searches are great to solve problems. For example, with this search, I got https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Precalculus_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.04%3A_Sum-to-Product_and_Product-to-Sum_Formulas

See formula 7.4.2

The solution to your problem is 6 cosx cos4x