A dip needle lies initially in the magnetic meridian when it shows an angle of dip `theta` at a place.The dip circle is rotated throught an angle x in the horizontal plane and then it shows an angle of dip `theta` .Then `(tantheta)/(tan theta)` is

Explanation

As `tan phi = (B_(v) /B_(H))` so when the needle is vertical, i.e., `phi = 90^@`, `B_(H) =0`.i.e., the plane of dip circle is perpendicular to the magnetic meridian. Now if the plane of dip circle is rotated by `alpha` from this position, the angle between magnetic meridian and plane of dip circle will be `(90^@- alpha)` and as angle of dip in this plane is `delta`,
`tan delta=B’_(v)/B’_(H)=B_(v)/B_(H)cos(90 - alpha)` or `tan delta=tan phi/sin alpha i.e..,phi=tan^(-1)(sin alpha tan delta)`