A) \[1\]
B) \[-1\]
C) \[2\]
D) \[-2\]
Correct Answer: C
Solution :
Given, \[\alpha +\beta =\frac{\pi }{4}\] \[\therefore \] \[\tan (\alpha +\beta )=\tan \left( \frac{\pi }{4} \right)=1\] \[\Rightarrow \] \[\tan \alpha +\tan \beta =1-\tan \alpha \,\,tan\,\beta \] \[\Rightarrow \]\[\tan \,\,\alpha +\tan \,\,\beta +\tan \,\alpha \,\tan \,\beta =1\] ?.(i) Now, \[(1+\tan \alpha )\,(1+\tan \beta )\] \[=1+\tan \alpha +\tan \beta +\tan \alpha \,\tan \beta \] \[=1+1=2\] [using Eq. (i)]
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