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BCECE Engineering BCECE Engineering Solved Paper-2001

  • question_answer
    If \[(A-B)=\frac{\pi }{4},\]then \[(1+\tan A)(1-\tan B)\] equal to:

    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                                 \[\tan (A-B)=\tan \frac{\pi }{4}\]                 \[\Rightarrow \]               \[\frac{\tan A-\tan B}{1+\tan \,A\,tan\,B}=1\] \[\Rightarrow \]               \[\tan A-\tan B=1+\tan A\tan B\] \[\Rightarrow \]               \[\tan A-\tan B-\tan \,A\,tan\,B\,+1=2\] \[\Rightarrow \]               \[\tan A(1-tan\,B)+(1-tan\,B)=2\] \[\Rightarrow \]               \[(1+tan\,A)(1-\tan B)=2\]


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