A) 1
B) 2
C) \[~-1\]
D) \[-2\]
Correct Answer: B
Solution :
Since, \[(A-B)=\frac{\pi }{4}\] Taking tan on both sides, we get \[\tan (A-B)=\tan \frac{\pi }{4}\] \[\Rightarrow \] \[\frac{\tan A-\tan B}{1+\tan \,A\,tan\,B}=1\] \[\Rightarrow \] \[\tan A-\tan B=1+\tan A\tan B\] \[\Rightarrow \] \[\tan A-\tan B-\tan \,A\,tan\,B\,+1=2\] \[\Rightarrow \] \[\tan A(1-tan\,B)+(1-tan\,B)=2\] \[\Rightarrow \] \[(1+tan\,A)(1-\tan B)=2\]You need to login to perform this action.
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