Question

If x+y=find the value of (1+tan x)(1+tan y).​

Answer 1

Answer:

Just this basic identity

tan(x+y)=tanx+tany1−tanxtany

And also tan45o=1

So ypur question

x+y=45o

Take tan on both sides

tan(x+y)=tan45o

tanx+tany1−tanxtany=1

tanx+tany=1−tanxtany

tanx+tanxtany+1+tany=2

tanx(1+tany)+1+tany=2

(tanx+1)(tany+1)=2

Henceproved

Thank you