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If A+B=45^(@), then (1+ tan A)(1+ tan B)...

If `A+B=45^(@)`, then `(1+ tan A)(1+ tan B)`=__________

Text Solution

Verified by Experts

Since `A+B=45^(@),tan(A+B)=tan45^(@)=1`
`rArr(tanA+tan B)/(1-tanAtanB)=1`
or `tanA+B=1-tanA tan B`
or `tan A+tanA tanB+ tanB= 1`
or ` tan A ( 1+ tan B) + tan B = 1 `
or `tanA(1+tanB)+1+tanB=1+1`
or `(1+tanA)(1+tanB)=2`
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