SOLUTION: prove that: 1-2 cos (72°)= (2cos(72°))^2

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Question 1142797: prove that: 1-2 cos (72°)= (2cos(72°))^2
Answer by math_helper(2461) About Me  (Show Source):
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Note that  +cos%2872%5Eo%29+=+%281%2F4%29%28%28sqrt%285%29%29+-+1%29++





RHS:  +%282cos%2872%5Eo%29%29%5E2+=+%282%28%281%2F4%29%28%28sqrt%285%29%29+-+1%29%29%29%5E2+

 = +%281%2F4%29%285%29+-+%282%2F4%29%28sqrt%285%29%29+%2B+%281%2F4%29+

 = ++%283%2F2%29+-+%281%2F2%29sqrt%285%29+



LHS:   +1+-+2cos%2872%5Eo%29+=++1+-+2+%28%281%2F4%29%28%28sqrt%285%29%29+-+1%29%29++ 

 = +1+-+%281%2F2%29%28sqrt%285%29+-+1%29+

 = +%283%2F2%29+-+%281%2F2%29%28sqrt%285%29%29+