Question

The graph of the function $\cos x\cos (x+2)-{\cos }^2(x+1)$ is

• 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 $(1,-{\sin }^{2}1)$
• D. a straight line passing through the point $(\frac{\pi }{2},-{\sin }^{2}1)$ and parallel to the X-axis

Answer 1

Answer: (D)

Let $y=\cos x\cos (x+2)-{\cos }^2(x+1)$
$=\cos (x+1-1)\cos (x+1+1)-{\cos }^2(x+1)$
$={\cos }^2(x+1)-{\sin }^{2}1-{\cos }^2(x+1)\Rightarrow y=-{\sin }^{2}1$
This is a straight line which is parallel to X-axis.
It passes through $(\pi /2,{\sin }^{2}1.)$