SOLUTION: Find the exact value by using a sum or difference identity. sin 75°

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Question 868199: Find the exact value by using a sum or difference identity.
sin 75°
Found 2 solutions by Edwin McCravy, htmentor:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Using the sum identity:

sin%28alpha%2Bbeta%29=sin%28alpha%29cos%28beta%29%2Bcos%28alpha%29sin%28beta%29

sin(75°) = sin(45°+30°) = sin(45°)cos(30°) + cos(45°)sin(30°) =

%28sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29%22%22%2B%22%22%28sqrt%282%29%2F2%29%281%2F2%29 %22%22=%22%22 sqrt%286%29%2F4%22%22%2B%22%22sqrt%282%29%2F4 %22%22=%22%22 %28sqrt%286%29%2Bsqrt%282%29%29%2F4

-----------------------------------

Using the difference identity:

sin%28alpha-beta%29=sin%28alpha%29cos%28beta%29-cos%28alpha%29sin%28beta%29

sin(75°) = sin(120°-45°) = sin(120°)cos(45°) - cos(120°)sin(45°) =

%28sqrt%283%29%2F2%29%28sqrt%282%29%2F2%29%22%22-%22%22%28-1%2F2%29%28sqrt%282%29%2F2%29 %22%22=%22%22 sqrt%286%29%2F4%22%22-%22%22%28-sqrt%282%29%2F4%29 %22%22=%22%22 sqrt%286%29%2F4%22%22%2B%22%22sqrt%282%29%2F4 %22%22=%22%22 %28sqrt%286%29%2Bsqrt%282%29%29%2F4 

Edwin

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Since 75 = 45 + 30, we can use the following identity:

This can be simplified to %28sqrt%283%29%2B1%29%2Fsqrt%288%29