write sin 6x + sin 2x as a product of sines and/or cosines

Answer 1

You want to use the following identity : sin (A) + sin (B) = 2sin((A+B)/2)*cos((A-B)/2)

in this case sin 6x + sin 2x ... A= 6x , B= 2x

Now, substitute in A and B into the identity formula above...

sin 6x + sin 2x = 2sin((6x+2x)/2)*cos((6x-2x)/2)

I'll let you simplify and get the final answer. Reach out if you want me to check it's correct! :)