JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer The graph of the function \[\cos x\ \cos (x+2)-{{\cos }^{2}}(x+1)\] is [IIT 1997 Re-Exam]

    A)            A straight line passing through \[(0,\,\,-{{\sin }^{2}}1)\]with slope 2     

    B)            A straight line passing through (0, 0)

    C)            A parabola with vertex \[{{75}^{o}}\]

    D)            A straight line passing through the point \[\left( \frac{\pi }{2},-{{\sin }^{2}}1 \right)\] and parallel to the x?axis               

    Correct Answer: D

    Solution :

               \[y=\cos (x+1-1)\cos (x+1+1)-{{\cos }^{2}}(x+1)\]                      \[={{\cos }^{2}}(x+1)-{{\sin }^{2}}1-{{\cos }^{2}}(x+1)=-{{\sin }^{2}}1\],                    which represents a straight line parallel to x-axis with \[y=-{{\sin }^{2}}1\] for all x and so also for \[x=\pi /2\].


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