यदि `alpha + beta = (pi)/(4)` हो, तो सिद्ध कीजिए कि - `(1+tan alpha)(1+tan beta)=2`.

Explanation

`because alpha + beta = pi//4, therefore " " tan (alpha + beta)=tan pi//4`
`rArr " " (tan alpha + tan beta)/(1-tan alpha.tan beta)=1 " " [because tan pi//4=1]`
`rArr " " tan alpha + tan beta = 1 - tan alpha. tan beta`
`rArr " " tan alpha + tan alpha.tan beta+tan beta =1`
`rArr " " tan alpha(1+tan beta)+1.(1+tan beta)=1+1`
`rArr " " (1+tan alpha) (1+ tan beta)=2. " "` इति सिद्धम्