If A + B = 225∘, then cotA1+cotA. cotB1+cotB =
[MNR 1974]
1
-1
0
1/2
cotA1+cotA. cotB1+cotB = 1(1+tanA)(1+tanB)
= 1tanA+tanB+1+tanAtanB
[ ∵ tan(A + B) = tan225∘]
⇒ tanA + tan B = 1 - tan A tan B
= 11−tanAtanB+1+tanAtanB = 12.