• # 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

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