The equation y= x(x+2)-^2(x+1) represents a straight line lying in:

Question

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

Accepted Answer

Using product-to-sum: $\sin x\sin(x+2) = \dfrac12[\cos(-2)-\cos(2x+2)]$, and $\sin^2(x+1)=\dfrac{1-\cos(2x+2)}2$:
$$y = \frac{\cos2}2-\frac{\cos(2x+2)}2 - \frac12+\frac{\cos(2x+2)}2 = \frac{\cos2-1}2 = -\sin^21$$

Since $y$ is a constant negative value (as $\sin^21>0$), this represents a horizontal line below the $x$-axis, lying in the third and fourth quadrants only.

Solutions · 1