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

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))`
`=>cos^2(A/2) = (b+c)/(2c)`
`=>(1+cosA)/2 = (b+c)/(2c)`
`=>cosA = (b+c)/(c) - 1`
`=>cosA = (b)/(c)`
`=>(b^2+c^2-a^2)/(2bc) = b/c`
`=>b^2+c^2-a^2 = 2b^2`
`=>a^2 + b^2 = c^2`
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