Two forces F₁ and F₂ are acting on a particle and the angle between them is theta.The angle between the resultant force and F₁ is alpha. Find tanalpha in terms of F₁,F₂ and theta.

here  you can see in fig                                                                                            
         
in triangle
OQN QN = F₂sin$\theta$ and ON = OP+PN (where PN = ​ F₂cos$\theta$)  =F₁+F₂cos$\theta$
                           
now using tan$\alpha$ =​$\frac{QN}{ON}=\frac{QN}{OP+PN}=\frac{F_2\sin \theta }{F_{1+}{F}_2\cos \theta }$