Can someone tell show me how to do this.

Show the product as a sum or difference

sin 6x cos 2x

(sin6x)(cos2x)

You will need to use the double-angle identities to expand both sin6x and cos2x.

As a hint, you will have to use sin(3*2x) for the double-angle of sine.

If you want to work on that, then we can critique your thinking.

ok thanks I'll work on that

To express the product sin(6x)cos(2x) as a sum or difference, we can use the trigonometric identity:

sin(A)cos(B) = (1/2) [sin(A + B) + sin(A - B)]

In this case, A = 6x and B = 2x. Plugging in these values, we get:

sin(6x)cos(2x) = (1/2) [sin(6x + 2x) + sin(6x - 2x)]

Simplifying further:

sin(6x)cos(2x) = (1/2) [sin(8x) + sin(4x)]

So, the product sin(6x)cos(2x) can be expressed as the sum of sin(8x) and sin(4x) divided by 2.