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Given, A=60° , B=30° then prove
cot(A-B) = ( cotAcotB + 1 )/ cotA - cotB
now Taking LHS :
cot(A-B) = cot( 60-30 )
= cot30
= √3 -------------------(1)
Taking RHS :
( cotAcotB + 1 )/ cotA - cotB = ( cot60.cot30 + 1 )/ cot30 - cot60
= [ (1/√3)(√3) + 1 ] /(√3 - 1/√3)
= [ 2 ] / ( 3 - 1 ) /√3
= (2)(√3)/2
= √3 ------------------(2)
So, from (1) and (2)
LHS = RHS
( Hence proved)
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