Question

Use the product-to-sum identities to rewrite the following expression as a sum or difference:

3sin(4x)cos(4x)
a) sin(8x)
b) sin(2x)
c) sin(4x)
d) sin(8x)+sin(2x)

Answer 1

The expression 3sin(4x)cos(4x) can be rewritten using the product-to-sum identities as (1/2)sin(8x), so the correct answer is option a) sin(8x).

Step-by-step explanation:

To rewrite the expression using the product-to-sum identities, we can use the formula:

sin(a)cos(b) = (1/2)[sin(a+b) + sin(a-b)]

In this case, a = 4x and b = 4x. Plugging these values into the formula, we get:

3sin(4x)cos(4x) = (1/2)[sin(4x+4x) + sin(4x-4x)]

Now simplify:

3sin(4x)cos(4x) = (1/2)[sin(8x) + sin(0)]

Since sin(0) = 0, the expression simplifies further:

3sin(4x)cos(4x) = (1/2)sin(8x)

Therefore, the answer is option a) sin(8x).