In a triangle ABC if b+c=3a then find th...

In a triangle `ABC` if `b+c=3a` then find the value of `cot(B/2)cot(C/2)`

Text Solution

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Given `b + c = 3a`
`cot.(B)/(2) cot.(C)/(2) = sqrt((s (s -b))/((s -a) (s -c))) sqrt((s (s -c))/((s - a)(s- b)))`..(i)
`= (s)/(s -a) = (2s)/(2s - 2a)`
`=(a + b + c)/(b + c -a) = (4a)/(2a) = 2` [by Eq. (i)]

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