A body of weight $W$ is suspended from a rigid support P by means of a massless string as shown in figure.  A horizontal force $F$ is applied at point  $O$ of the rope. The system is in equilibrium when the string makes an angle with  $\theta$  the vertical. If the tension in the string is $T$,

The mass is in equilibrium at point O under the action of the concurrent forces F, T and W=mg.

Therefore, as shown in fig. 5.100, the horizontal component T sin $\theta$ of tension T must balance with force F and the vertical component T cos $\theta$ must balance with weight W=mg.

Thus  F=Tsin $\theta$……….(1)

 and     W=T cos $\theta$ …….(ii)

 Squaring Eqs. (i) and (ii) and adding we get

  $T^2=W^2+F^2$

Dividing (i) by (ii) we get F=W tan $\theta$

Hence the correct choices are (a), (c) and (d)