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

Show Answer

Solution:

  1. 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 $\left(\pi / 2,-\sin ^{2} 1\right)$.



NCERT Chapter Video Solution

Dual Pane