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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 19

  • question_answer
    If \[{{\tan }^{-1}}\left( -\alpha +\theta -\frac{{{\theta }^{3}}}{3!}+\frac{{{\theta }^{5}}}{5!}-\frac{{{\theta }^{7}}}{7!}+...\infty  \right)+{{\cot }^{-1}}\]\[\left( \alpha -1+\frac{{{\theta }^{2}}}{2!}-\frac{{{\theta }^{4}}}{4!}+...\infty  \right)=\frac{\pi }{2},\]then maximum value of \[\alpha \] equals to

    A) \[-\frac{1}{\sqrt{2}}\]                            

    B) \[\frac{1}{2}\]

    C) \[\frac{1}{\sqrt{2}}\]     

    D)        \[1\]

    Correct Answer: C

    Solution :

    [c] Given equation is \[{{\tan }^{-1}}(-\alpha +\sin \theta )+{{\cot }^{-1}}(\theta -\cos \theta )=\frac{\pi }{2}\] \[\Rightarrow -\alpha +\sin \theta =\alpha -\cos \theta \]\[\Rightarrow \,\,2\alpha =\sin \theta +\cos \theta \in \left[ -\sqrt{2},\sqrt{2} \right]\] 


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