JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 69) If \[{{\theta }_{1}},\,\,{{\theta }_{2}}\] are the solutions of the equation\[2{{\tan }^{2}}\theta -4\tan \theta +1=0\], then \[\tan ({{\theta }_{1}}+{{\theta }_{2}})\]is equal to

    A) \[-4\]                           

    B) \[4\]

    C) \[1\]                             

    D) \[2\]

    Correct Answer: B

    Solution :

     Let \[\tan {{\theta }_{1}},\,\,\tan {{\theta }_{2}}\] be the roots of the\[2{{\tan }^{2}}\theta -4\tan \theta +1=0\] equation. Thus \[\tan {{\theta }_{1}}+\tan {{\theta }_{2}}=4/2=2;\,\,\tan {{\theta }_{1}}\tan {{\theta }_{2}}=1/2\]. Now\[\tan ({{\theta }_{1}}+{{\theta }_{2}})=[(\tan {{\theta }_{1}}+\tan {{\theta }_{2}})/(1-\tan {{\theta }_{1}}\tan {{\theta }_{2}})]\]\[=2/[1-(1/2)]=4\].

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