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If in a triangle ABC ,b +c=4a then cot(B...

If in a triangle ABC ,b +c=4a then `cot(B/2)cot(C/2)` is equal to

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In a triangle ABC if cot(A/2)cot(B/2)=c, cot(B/2)cot(C/2)=a and cot(C/2)cot(A/2)=b then 1/(s-a)+1/(s-b)+1/(s-c)=