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If cos (A /2) =sqrt((b+c)/(2c)) , then ...

If `cos (A /2) =sqrt((b+c)/(2c))` , then prove that `a^2+b^2=c^2dot`

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`cos.(A)/(2) = sqrt((b + c)/(2c))`
`rArr (s(s -a))/(bc) = (b + c)/(2c)` [squaring]
or `2s(2s - 2a) = 2b (b + c)`
or `(b + c + a) (b + c - a) = 2b^(2) + 2bc`
or `(b+ c)^(2) - a^(2) = 2b^(2) + 2bc`
or `c^(2) = a^(2) + b^(2)`
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