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If A + B = (pi)/(4), then prove that (1 ...

If A + B = `(pi)/(4)`, then prove that (1 + tan A) (1 + tan B) = 2

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Verified by Experts

We have, `A+B=pi/4`
`tan(A+B)=tanpi/4`
`(tanA+tanB)/(1-tanAtanB)=1`
`rArr tanA+tanB=1-tanAtanB`
`rArr tanA+tanB+tanAtanB=1`
`rArr 1+tanA+tanB+tanAtanB=2`
`rArr (1+tanA)+tanB(1+tanA)=2`
`rArr (1+tanA)(1+tanB)=2`
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AAKASH INSTITUTE ENGLISH-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
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