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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

  • question_answer
    If\[tan\text{ }A-tan\text{ }B=x\]and\[cot\text{ }B-cot\text{ }A=y,\]then \[cot(A-B)\]is equal to

    A)  \[x+y\]            

    B)  \[x+\frac{1}{y}\]

    C)  \[\frac{1}{x}+\frac{1}{y}\]           

    D)  \[x+2y\]

    Correct Answer: C

    Solution :

     \[\cot B-\cot A=y\]\[\Rightarrow \]\[\frac{\tan A-\tan B}{\tan A.\tan B}=y\] \[\frac{x}{y}=\tan A.\tan B\] \[\therefore \]Now, \[\cot (A-B)=\frac{1}{\tan (A-B)}\] \[=\frac{1+\tan A.\tan B}{\tan A-\tan B}\] \[=\frac{1+x/y}{x}=\frac{1}{x}+\frac{1}{y}\]


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