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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
                If\[\tan x=\frac{3}{4},\pi <x<\frac{3\pi }{2}\],then the value of \[\cos \frac{x}{2}\]is

    A) \[-\frac{1}{\sqrt{10}}\]  

    B) \[\frac{3}{\sqrt{10}}\]

    C) \[\frac{1}{\sqrt{10}}\]               

    D) \[-\frac{3}{\sqrt{10}}\]

    Correct Answer: A

    Solution :

    [a]: Since x lies in 3rd quadrant. So, cos x and \[\cos \frac{x}{2}\]are negative Now, \[\tan x=\frac{3}{4}\Rightarrow \cos x=-\frac{4}{5}\] Also,\[{{\cos }^{2}}\frac{x}{2}=\frac{1}{2}\{cos\,x+1\}=\frac{1}{2}\left\{ -\frac{4}{5}+1 \right\}=\frac{1}{10}\] \[\Rightarrow \]\[\cos \frac{x}{2}=\frac{-1}{\sqrt{10}}\]


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