SOLUTION: write the difference sin 8t - sin 2t as a product

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Question 464315: write the difference sin 8t - sin 2t as a product
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
sin(8t) - sin(2t)

The average of 8t and 2t is 5t.
8t is 3t more than 5t and 2t is
3t less than than 5t. So the above 
becomes 

                       sin(5t+3t) - sin(5t-3t)

Then we use the formulas: sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)

and                    sin(5t+3t) - sin(5t-3t)
becomes:

[sin(5t)cos(3t) + cos(5t)sin(3t)] - [sin(5t)cos(3t) - cos(5t)sin(3t)]

Remove the brackets:

  sin(5t)cos(3t) + cos(5t)sin(3t) - sin(5t)cos(3t) + cos(5t)sin(3t)

Collect like terms, the first and 3rd terms cancel out
and the other two add to make 2 of them and we end up with

                          2cos(5t)sin(3t)

Edwin