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.