 In this video, we present the solution to question number six for practice exam number two for math 1060, in which case we're asked to rewrite the product 10 sine of 5x times sine of 3x as a sum or difference and then simplify it possible. So we have a product and we want to switch it to a sum or difference, so we need to use the appropriate product to sum trigonometric identity. Notice this has the form sine sine. So as we consult our formula sheet, we then see that sine of a sine of B, which of course let's be clear here sine or a excuse me is 5x and angle B is equal to 3x here. According to our formula sheet, sine of a sine of B is equal to one half negative cosine of a plus B. And then we get plus cosine of a minus B. And so this would be the identity that's appropriate to use in this example here. So let's plug in the specific values. So we have 10 times the sine of 5x sine of 3x becomes negative cosine of we're going to add the angles together 5x plus 3x is an 8x. And then we're going to get, oh, I forgot the one half there. So there should be one half there. And then we get cosine of their difference for which we're going to take 5x minus 3x, which is a 2x like so. Notice, of course, 2 goes into 5, 10, excuse me, 2 goes into 10, 5 times. So we're going to get a 5 out in front. Again, negative cosine of 8x, we're going to get cosine of 2x right here. And then notice if we distribute the 5 onto both pieces, then we see that choice A would be the correct simplified sum or difference if you want to call it that of the product we started off with.