SOLUTION: express the difference sin(pi/4) - sin(pi/6) as a product.

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Question 1051343: express the difference sin(pi/4) - sin(pi/6) as a product.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We'll use a trig identity. Specifically, we'll use this trig identity:

sin%28A%29+-+sin%28B%29+=+2%2Acos%28%28A%2BB%29%2F2%29%2Asin%28%28A-B%29%2F2%29

where in this case, A+=+pi%2F4 and B+=+pi%2F6


Note: see page 2 under the "Sum to Product Formulas" section


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sin%28A%29+-+sin%28B%29+=+2%2Acos%28%28A%2BB%29%2F2%29%2Asin%28%28A-B%29%2F2%29


Plug in A+=+pi%2F4 and B+=+pi%2F6











sin%28pi%2F4%29+-+sin%28pi%2F6%29+=+2%2Acos%285pi%2F24%29%2Asin%28pi%2F24%29


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The final answer is 2%2Acos%285pi%2F24%29%2Asin%28pi%2F24%29