Question

show that co-efficient of static friction is numerically equal to the tangent of the angle of friction ​

Answer 1

The coefficient of static friction is equal to the tangent of the angle at which the objects slide. A similar method can be used to measure μk.

To do that you give the top object a push as you increase the angle. When the top object keeps sliding with constant velocity, the tangent of that angle is equal to μk.