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If A+B=pi/4, prove that: (1+tanA)(1+ta...

If `A+B=pi/4`, prove that:
`(1+tanA)(1+tanB)=2`

Text Solution

Verified by Experts

`A+B=pi/4`
`rArr tan(A+B)=tanpi/4`
`rArr (tanA+tanB)/(1-tanAtanB)=1`
`rArr tanA+tanB=1-tanAtanB`
`rArr tanA+tanB+tanAtanB=1`
`rArr 1+tanA + tanBtanB=2`
`rArr (1+tanA)(1+tanB)=2` Hence proved.
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