First slide

Equation of line in Straight lines

Question

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

Moderate

A

2^nd and 3^rd quadrant
B

1^st, 2^nd and 4^th quadrant
C

1^st, 3^rd and 4^th quadrant
D

3^rd and 4^th quadrant

Solution

$y = \frac{1}{2} [\cos 2 - \cos (2 x + 2)] - \frac{1}{2} [1 - \cos (2 x + 2)]$
$= \frac{1}{2} [\cos (2) - 1] = - \sin^{2} (1) < 0$
$y < 0 \Rightarrow 3^{r d} & 4^{t h}$ quadrant

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