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Question

If A+B=45o, prove that (cotA1)(cotB1)=2

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Solution

Given A+B=45

cot(A+B)=cot45

cotAcotB1cotA+cotB=1

cotAcotB1=cotA+cotB

cotAcotBcotAcotB=1

cotAcotBcotAcotB+1=2

cotA(cotB1)(cotB1)=2

(cotA1)(cotB1)=2

Hence proved.

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