2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

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

    A)  \[1\]                                    

    B)  \[\frac{1}{2}\]

    C)  \[-1\]                   

    D)         \[-2\]

    E)  \[2\]

    Correct Answer: E

    Solution :

    Given, \[A+B=45{}^\circ \] \[\Rightarrow \]               \[\cot (A+B)=1\] \[\Rightarrow \]               \[\frac{\cot A\cot B-1}{\cot A+\cot B}=1\] \[\Rightarrow \]               \[\cot A\cot B-(\cot A+\cot B)=1\]           ?..(i) Now, \[(\cot A-1)(\cot B-1)=\cot A\cot B\]                                                 \[-(\cot A+\cot B)+1\] \[=1+1=2\]               [from Eq. (i)]


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