SOLUTION: Please help me solve this equation: Exact value of cos(2cos^-1(3/4))

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Question 675353: Please help me solve this equation: Exact value of cos(2cos^-1(3/4))
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to understand that the inverse cosine function returns an angle. So your expression is the cos of twice some angle. We can use the cos(2x) formula to rewrite your expression. cos(2x) has three variations:
cos%282x%29+=+cos%5E2%28x%29+-+sin%5E2%28x%29
cos%282x%29+=+2cos%5E2%28x%29+-+1
cos%282x%29+=+1+-+2sin%5E2%28x%29
Since the angle is expressed in terms of inverse cos, I'm going to choose the middle ("All cos") variation of cos(2x):
cos%282cos%5E%28-1%29%283%2F4%29%29+=+2cos%28cos%5E%28-1%29%283%2F4%29%29+-+1
The cos%28cos%5E%28-1%29%283%2F4%29%29 part of this is "the cos of an angle whose cos is 3/4. I hope it is obvious that this would be 3/4. So now we have: