if x-y=π/4,prove that(1+tanx)(1+tany)=2tanx Share with your friends Share 8 Tanveer Sofi answered this We are given thatx-y=π4⇒x=π4+yWe know thattanA+B=tan A- tan B1-tan A. tan BTherefore,tanx=tanπ4+y=tanπ4+tan y1-tanπ4. tan y=1+tan y1-tan y As tanπ4=1⇒tan x1-tan y=1+tan y⇒tan x-tan x. tan y=1+tan y⇒tan x=1+tan y+tan x. tanyAdding tan x to both sides, we get2 tan x=1+tan x+tan y+tan x. tan y⇒2 tan x=1+tan x+tan y1+tan x=1+tan x1+tan y⇒1+tan x1+tan y=2 tan x. 25 View Full Answer