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Question:

The equation y = sin x sin(x+2) - sin²(x+1) represents a straight line lying in?

Second and third quadrants only

First, third and fourth quadrants

First, second and fourth quadrants

Third and fourth quadrants only

Solution:

Correct option is B. Third and fourth quadrants only
2y = 2sin x sin(x+2) - 2sin²(x+1)
2y = cos 2 - cos(2x+2) - (1 - cos(2x+2)) = cos 2 - 1
2y = -2sin²1
y = -sin²1 ≤ 0.