Question

(h
cot3A.cot2A + 1
cot2A - cot3A
= cota​

Answer 1

L.H.S. = cot A cot 2A – cot 2A cot 3A – cot 3A cot A

= cot A cot 2A – cot 3A (cot 2A + cot A)

= cot A cot 2A – cot (2A + A) (cot 2A + cot A)

= cotA cot2A - [ (cot2A cotA - 1) / (cotA + cot2A) ] (cot2A + cotA)

[ Since cot(A+B) = (cotA cotB - 1) / (cotA + cotB) ]

= cot A cot 2A – (cot 2A cot A – 1)

= 1 = R.H.S.