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If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that tan θ = (x2y1 - x1y2)/(x1x2 + y1y2) and cos θ = (x1y2 + y1y2)/√(x12 + y12) √(x22 + y22)

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We need to prove:

Let us assume A (x1, y1) and B (x2, y2) be the given points and O be the origin.

Slope of OA = m1 = y1×1

Slope of OB = m2 = y2×2

It is given that θ is the angle between lines OA and OB.

Hence proved.

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