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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    The number of solution(s) of the equation \[2\,{{\tan }^{2}}x+2\,{{\tan }^{4}}x-2\,{{\sec }^{4}}\,x\,{{\sin }^{2}}x-3=0\] in \[\left( 0,\,\frac{\pi }{2} \right)\] is

    A)  0                                

    B)  1                 

    C)  3                                

    D)  4

    Correct Answer: A

    Solution :

     The given equation can be written as -\[2\,{{\tan }^{2}}x+{{\tan }^{4}}x+{{\tan }^{4}}x\] \[-2{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[2\,{{\tan }^{2}}x+{{({{\sec }^{2}}x-1)}^{2}}+{{\tan }^{4}}x\] \[-2\,{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[2\,{{\tan }^{2}}x+{{\sec }^{4}}x+1-2\,{{\sec }^{2}}x\] \[+{{\tan }^{4}}x-2\,{{\sec }^{2}}x\,{{\tan }^{2}}x-3=0\] \[\Rightarrow \] \[{{({{\sec }^{2}}x-{{\tan }^{2}}x)}^{2}}=4\] \[\Rightarrow \]            \[1\ne 4\] Hence, no solution exists.


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