# The slope of a line is double of the slope of another line. If tangents of the angle between them is , find the slopes of the other line.

Given, The tangent of the angle between them is To Find Slope of the other line.

Assumption: The slope of line m1 = x, and m2 = 2x

Formula used: Explanation: We have tan given, then Case 1: 2x2 + 1 = 3x – 6x

2x2 + 3x + 1 = 0

2x2 + 2x + x + 1 = 0

2x(x + 1) + 1(x + 1) = 0

(2x + 1)(x + 1) = 0

x = – 1, Case 2: 2x2 + 1 = 3x

2x2 – 3x + 1 = 0

2x2 – 2x – x + 1 = 0

2x(x – 1) – 1(x – 1) = 0

(2x – 1)(x – 1) = 0

x = 1, Hence, The slope of other line is either 1, or – 1, .

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