Rewrite the sum as a product using a sum-to-product identity.
A) 2cos(3$\alpha$)sin(2$\alpha$)
B) 2sin(3$\alpha$)cos(2$\alpha$)
C) 2cos(3$\alpha$)cos(2$\alpha$)
D) 2sin(3$\alpha$)sin(2$\alpha$)

Question

Rewrite the sum as a product using a sum-to-product identity. 
A) 2cos(3$\alpha$)sin(2$\alpha$) 
B) 2sin(3$\alpha$)cos(2$\alpha$) 
C) 2cos(3$\alpha$)cos(2$\alpha$) 
D) 2sin(3$\alpha$)sin(2$\alpha$)

Quizplus · Accepted Answer

The sum-to-product identity for cosines is:

cos(x) + cos(y) = 2cos[(x+y)/2]cos[(x-y)/2]

Using this identity, the given sum can be rewritten as:

2sin(7α)cos(4α) = 2(cos(3α+4α) + cos(7α-4α))/2

Simplifying:

= 2cos(3α)cos(2α) + 2cos(3α)cos(2α)

= 2cos(3F1F1F1S1αF1F1F10)cos(2F1F1F1S1αF1F1F10)

Therefore, the correct answer is C.

Rewrite the Sum as a Product Using a Sum-To-Product Identity α\alphaα

Rewrite the Sum as a Product Using a Sum-To-Product Identity $\alpha$