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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If\[f(\theta )=\tan \theta ,\]then the value of\[\frac{f(\theta )-f(\phi )}{1+f(\theta )f(\phi )}\]is

    A)  \[f(\theta )+f(\phi )\]

    B)  \[f(\theta -\phi )\]

    C)  \[f\left( \frac{\theta }{\phi } \right)\]

    D)  \[\theta -\phi \]

    Correct Answer: B

    Solution :

     Given,\[f(\theta )=\tan \theta ,\]then \[f(\phi )=\tan \phi \] \[\therefore \] \[\frac{f(\theta )-f(\phi )}{1+f(\theta )f(\phi )}=\frac{\tan \theta -\tan \phi }{1+\tan \theta \tan \phi }\] \[=\tan (\theta -\phi )\] \[=f(\theta -\phi )\]


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