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Good students. welcome to part 4 of the sum and difference identities. We're going to be going over one example. So lets go ahead and write down the question. Example 1. Find Sin A minus B Given that Sin A equals 7 over 8 with pie over 2 is less than A. and A is less Than pie. and Cos B equals 6 over 7 with a negative pie over two is less than B And B is less than zero. Alright so lets go ahead and find this. the first thing we are going to do is write down the formula for the difference identities of Sin. So we have Sin A - B equals Sin A Cos B. If the trig functions are different then the sign will stay the same as this one. Minus Cos A Sin B. So lets see what we know. We were provided with Sin A. So we have Sin A we are also provided with Sin B. So in order for us to find Sin A minus B, We need to determine what Sin A is. and what Sin B is. So in order to do that we need to make use of the Path and identity which is Sin Squared theta plus Cos squared Theta equal 1. I know that from this identity ill end up with Sin theta is equal to plus of minus the square root of 1 minus Cos squared theta. This is one variation of the Pythagoras and identity when solving explicitly for Sin. And also know that Cos theta equals plus or minus the square root of one minus Sin squared theta. So this is going to tell me that with Cos i can find Sin and with this one it tells me you can find Sin with Cos. So lets find the component or ingredients that we need to generate Sin A minus B The first thing we need, lets look for Cos A. So we know that Sin A equals 7 over 8 so, Cos A is going to be plus or minus the square root of one minus Sin squared A. We were using this formula while we were replacing the thetas from A. we're going to plug in the value of Cos A which is 7 over 8. so we're going to have Co
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