JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    lf \[\tan (\pi cos\theta )=cot(\pi sin\theta ),\] then \[\cos \theta ,\sin \theta \] are roots of equation

    A) \[4{{x}^{2}}-4x-1=0\]     

    B) \[4{{x}^{2}}-2x-1=0\]

    C) \[8{{x}^{2}}-4x-3=0\]     

    D)  None of these

    Correct Answer: C

    Solution :

    \[\tan (\pi cos\theta )=cot(\pi sin\theta )\] \[\Rightarrow \]\[\pi cos\theta =n\pi +\frac{\pi }{2}-\pi \sin \theta \] \[\Rightarrow \]\[\sin \theta +\cos \theta =n+\frac{1}{2};n\in I\] \[\Rightarrow \]\[\sin \theta +\cos \theta =\frac{1}{2}or-\frac{1}{2}\] \[\Rightarrow \]\[\sin \theta \cos \theta =-\frac{3}{8}\] \[\therefore \]\[\sin \theta \]and\[\cos \theta \]are roots of \[{{x}^{2}}\pm \frac{1}{2}\times -\frac{3}{8}=0\]

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