**To prove:**

tan θ = ** \(\frac{x_2y_1 - x_1y_2}{x_1x_2 + y_1y_2}\) **and cos θ = \(\frac{x_1x_2 + y_1y_2 }{\sqrt{x_1^2 + y_1^2 }\sqrt{x_2^2 + y^2_2}}\)

**Assuming: **

A (x_{1}, y_{1}) and B (x_{2}, y_{2}) be the given points and O be the origin.

**Explanation:**

Slope of OA = m_{1} = y_{1}x_{1 }

Slope of OB = m_{2} = y_{2}x_{2}

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

Now, As we know that cos θ = \(\sqrt{\frac{1}{1+ tan^2θ}}\)