Two ideal electric dipoles \(A\) and \(B\) having their dipole moment \(p_{1}\) and \(p_{2}\) respectively are placed on a plane with their centres at \(O\) as shown in the figure. At point \(C\) on the axis of dipole \(A\), the resultant electric field is making an angle of \(37^{\circ}\) with the axis. The ratio of the dipole moment of \(A\) and \(B, \frac{P_{1}}{P_{2}}\) is \(....\) (take \(\left.\sin 37^{\circ}=\frac{3}{5}\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.