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SSC Sample Paper Mock Test-14 SSC CGL Tear-II Paper-1

  • question_answer
    If \[A+B+=45{}^\circ ,\]then\[(1+\tan A)(1+\tan B)\]is equal to

    A) 1

    B)  \[-\,\,1\]

    C)  2

    D)  \[-\,\,2\]

    Correct Answer: C

    Solution :

    \[(1+\tan A)(1+\tan B)=(1+\tan A)[1+\tan \,\,(45{}^\circ -A)]\]    \[=(1+\tan A)\left[ 1+\frac{\tan 45{}^\circ -\tan A}{1+\tan 45{}^\circ \tan A} \right]\]
    \[=(1+\tan A)\left[ 1+\frac{1-\tan A}{1+\tan A} \right]\]
    \[=(1+\tan A)\left[ 1+\frac{\tan A+1-\tan A}{1+\tan A} \right]\]
    \[=(1+\tan A)\left[ \frac{2}{1+\tan A} \right]=2\]


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