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$If \tan α = {(1 + 2^{- x})}^{- 1} and \tan β = {(1 + 2^{x + 1})}^{- 1} . Then α + β =$

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Correct option is B

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

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

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$If \tan α = {(1 + 2^{- x})}^{- 1} and \tan β = {(1 + 2^{x + 1})}^{- 1} . Then α + β =$