cot A cot 2A - cot 2A cot 3A - cot 3A cot A = 1
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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.
⚡Hope it will help you.⚡
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