Question

IF A+B=45° show that cot(A-1)cot (B-1)=2and hence use the value of cot 22.5​

Answer 1

Answer:

Correct option is

A

2

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