If  tanα=1+2-x-1 and  tanβ=1+2x+1-1 . Then α+β=

We have tanα=2x+12x-1⇒tanα=2x2x+1Also tanβ=1+2x·2-1⇒tanβ=11+2x·2Now tan(α+β)=2x2x+1+11+2x·21-2x2x+1·11+2x·2⇒tan(α+β)=tt+1+12t+11-tt+111+2t     where t=2x=(2t+1)t+t+1(t+1)(1+2t)-t        =2t2+t+t+1t+2t2+1+2t-t=1 ⇒α+β=π4