SOLUTION: Evaluate cos(2sin^-1(4/5))

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Question 365266: Evaluate cos(2sin^-1(4/5))
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = 2sin^1(4/5). Then A/2 = sin^1(4/5), or sin%28A%2F2%29+=+4%2F5. We have to find cosA. But from the identity cos+A+=+1-2sin%5E2%28A%2F2%29 we get cosA+=+1-2%2A%284%2F5%29%5E2+=+1-2%2A%2816%2F25%29+=+1-32%2F25+=+-7%2F25