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Question

If y=(1+tanA)(1tanB) where AB=π4, then (y+1)y+1

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Solution

AB=π4tan(AB)=tanπ4
tanAtanB1+tanAtanB=1
tanAtanBtanAtanB=1
tanAtanBtanAtanB+1=2
(1+tanA)(1tanB)=2y=2(y+1)y+1=33=27

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