A) A straight line passing through \[(0,-si{{n}^{2}}1)\] with slope 2
B) A straight line passing through (0, 0)
C) A parabola with vertex \[(1,-si{{n}^{2}}1)\]
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 :
[d] \[y=\frac{1}{2}[cos(2x+2)+cos2-\{1+cos(2x+2)\}]\] Or \[y=-\frac{1}{2}\,(1-cos2)=-si{{n}^{2}}1\] i.e. constant \[\therefore \]Graph is a line parallel to x-axis. Also when \[x=\frac{\pi }{2},y=-{{\cos }^{2}}\left( \frac{\pi }{2}+1 \right)=-{{\sin }^{2}}1\] and hence it passes through the point \[\left( \frac{\pi }{2},-{{\sin }^{2}}1 \right)\]
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