if A + B = 45 then prove:
( 1 + cotA) (1 + cotB) = 2cotBcotA
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Correct option is A)
Given A+B=45
∘
⟹cot(A+B)=cot45
∘
⟹
cotA+cotB
cotAcotB−1
=1
⟹cotA+cotB−cotAcotB=−1
⟹cotA+cotB−cotAcotB−1=−2
⟹cotA(1−cotB)−(1−cotB)=−2
⟹(cotA−1)(1−cotB)=−2
⟹(cotA−1)(cotB−1)=2
So m=2
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