If in ` A B C ,A C` is double of `A B` , then the value of `cot(A/2)cot((B-C)/2)` is equal to `1/3` (b) `-1/3` (c) `3` (d) `1/2`

Explanation

b=2c-(1)

`tan((B-C)/2)=(b-c)/(b+c)cot(A/2)`

`cot(A/2)cot((B-C)/2)=(b+c)/(b-c)=(2c+c)/(2c-c)=3`.