J & K CET Engineering J and K - CET Engineering Solved Paper-2014

  • question_answer
    Find the value of \[\sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1\]

    A)  \[1/x\]             

    B)  \[x\]

    C)  \[1/{{x}^{2}}\]             

    D)  \[2x/(1+{{x}^{2}})\]

    Correct Answer: D

    Solution :

    \[\sin (2{{\tan }^{-1}}x)=\sin \left( {{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}} \right)\] \[=\frac{2x}{1+{{x}^{2}}},-1\le x\le 1\]


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