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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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Knowledge Check

  • If b+c=3a " then the value of " cot ""B/2 cot ""C/2=

    A
    1
    B
    2
    C
    `sqrt3`
    D
    `sqrt2`

  • In a triangle ABC, right angled at C, the value of cot A + cot B is

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    `c^2/(ab)`
    B
    a+b
    C
    `a^2/(bc)`
    D
    `b^2/(ac)`

  • In a triangle ABC, right angled at C, the value of cot A + cot B is

    A
    `c^2/(ab)`
    B
    a+b
    C
    `a^2/(bc)`
    D
    `b^2/(ac)`

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