A block of mass $m$ is placed on a wedge of mass $M$ and angle $\theta$. The wedge is placed on a smooth horizontal surface. If the coefficient of friction between the block and the wedge is $\mu$, what horizontal force $F$ must be applied to the wedge so that the block does not slide relative to the wedge?

1. A.$(M+m)g\frac{\sin \theta +\mu \cos \theta }{\cos \theta -\mu \sin \theta }$
2. B.$(M+m)g\frac{\sin \theta -\mu \cos \theta }{\cos \theta +\mu \sin \theta }$
3. C.$mg\frac{\sin \theta +\mu \cos \theta }{\cos \theta -\mu \sin \theta }$
4. D.$(M+m)g\tan \theta$