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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