Question

establish the identity:

cot(A-B)= cotAcotB+1/cotB-cotA

thanks for any help at all

Answer 1

Is the final term
1/(cotB-cotA) or
(1/cotB)-cotA ??

Is the numerator term (cotA cotB +1) or 1 ?

When you write equations like that, we can't tell what you mean.

I suggest you start with the identities for cos (A-B) and sin (A-B) and take the ratio of the two.

Answer 2

cos(a+b)/sin(a+b)=
cosacosb+sinasinb/sinacosb-cosasinb
multiplying and dividing by sinasins then it becomes
cotacotb+1/cotb-cota