Question

tanA + tanB = a and cotA + cotB = b prove that cot(A+B) = 1/a - 1/b

Answer 1

here cot(a+b)= cota.cotb-1/cota+cotb

Answer 2

tanA + tanB = A --------(I) & cotA + cotB = B-------(II) 
or from (I) 1/cotA + 1/cotB =A 
or { cotA + cotB}/cotA cotB = A 
or B/cotA cotB = A 
or cotA cotB = B/A-------------------------------------... 
so cot( A+B ) =cotA * cotB -1/ cotA+ cotB 
= { B/A -1}/B 
= 1/A - 1/B