Question

if α+β=π/4,prove that (1+tanα)(1+tsnβ)=2

Answer 1

Given α+ß=45
Take tan on both sides
Tan(α+ß) =tan45
Tanα+Tanß/ 1- tanαtanß =1
Tanα+ tanß =1-tanα+tan ß
Now add 1 on both sides
1 +tanα+ tanß + tanαtanß =1+1
1+tanα+tanß+tanαtanß=2
1+tanα+tanß(1+tanα)=2
(1+ tanα)(1+ tanß)=2