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 $\Bigg(\frac{\pi}{2}, -\sin^2 1\Bigg)$ 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 $(\pi/2, \sin^2 1.)$