Question

The equation $y=\sin x\sin (x+2)-{\sin }^2(x+1)$ represents a straight line lying in :

• A. second and third quadrants only
• B. third and fourth quadrants only
• C. first, third and fourth quadrants
• D. first, second and fourth quadrants

Answer 1

Answer: (B)

$2y=2\sin x\sin \left(x+2\right)-2{\sin }^2\left(x-1\right)$
$2y=\cos 2-\cos \left(2x+2\right)-\left(1-\cos \left(2x+2\right)\right)$
$=\cos 2-1$
$2y=-2{\sin }^2\frac{1}{2}$
$y=-{\sin }^2\frac{1}{2}\le 0$