# The equation $y=\sin x\sin \left ( x+2 \right )-\sin ^{2}\left ( x+1 \right )$ represents a straight line lying in :  Option 1) first, third and fourth quadrants  Option 2) third and fourth quadrants only Option 3) first, second and fourth quadrants Option 4) second and third quadrants only

$y=\sin x\sin \left ( x+2 \right )-\sin ^{2}\left ( x+1 \right )$

$2y=2\sin x\sin \left ( x+2 \right )-2\sin ^{2}\left ( x+1 \right )$

$=\cos 2-\cos \left ( 2x+2 \right )-\left ( 1-\cos \left ( 2x+2 \right ) \right )$

$=\cos 2-1$

$y=\frac{\cos 2-1}{2}=-\sin^21$

Option 1)

Option 2)

Option 3)