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 = \cos2 -\cos\left(2x+2\right)-\left(1-\cos\left(2x+2\right)\right)$
$ =\cos2-1 $
$ 2y =-2 \sin^{2} \frac{1}{2} $
$ y = - \sin^{2} \frac{1}{2} \le0 $