Straight Line and Pair of Straight Lines 1 Question 34
34. The graph of the function $\cos x \cos (x+2)-\cos ^{2}(x+1)$ is
$(1997,2 M)$
(a) a straight line passing through $\left(0,-\sin ^{2} 1\right)$ with slope 2
(b) a straight line passing through $(0,0)$
(c) a parabola with vertex $\left(1,-\sin ^{2} 1\right)$
(d) a straight line passing through the point $\frac{\pi}{2},-\sin ^{2} 1$ and parallel to the $X$-axis
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Solution:
- Let $y=\cos x \cos (x+2)-\cos ^{2}(x+1)$
$$ \begin{aligned} & =\cos (x+1-1) \cos (x+1+1)-\cos ^{2}(x+1) \\ & =\cos ^{2}(x+1)-\sin ^{2} 1-\cos ^{2}(x+1) \Rightarrow y=-\sin ^{2} 1 \end{aligned} $$
This is a straight line which is parallel to $X$-axis.
It passes through $\left(\pi / 2,-\sin ^{2} 1\right)$.
