angle of dip is θ₁at a place on the earth,magnetic latitude is θ₂.prove that 2cotθ₁=cotθ₂

The angle of dip at a place on the earth gives the direction of earth magnetic field.
Angle of dip or magnetic inclination is the angle of made by the earth total magnetic field
B
with the horizontal direction in the magnetic meridian is called angle of dip(S) at an place. Its value is different for different places. Experimentally ; take a compass (dip) or needle, pivoted horizontally so that it is free to rotate in vertical plan conceding with the magnetic meridian. It orients itself so that its N-pole finally points exactly in direction of the earth's total magnetic field. The angle between the horizontal and final direction of the dip needle gives the angle of dip at the location. its this experimental setup, magnetic (dip) needle remain (rests) horizontally so, angle of dip zero at magnetic meridian.
Hence, the answer is the direction of the earth's magnetic field.