How do I solve this equation?


I'm not sure that I have the knowledge required to solve this problem yet, I have tried and can get it to: $$\sin(2v)(1+3\cos(40^\circ))=3\sin(40^\circ)\cos(2v)-\sin(40^\circ)$$

However, I doubt it has brought me any closer to a solution, and would be happy if you could provide me with a full solution. Thanks!



Using Prosthaphaeresis Formula $(\sin C+\sin D)$,



So, either $\cos(v-20^\circ)=0$ or $\sin(v+20^\circ)+3\sin(v-20^\circ)=0$

But $\cos(v-20^\circ)=0$ will make the left hand side of the given expression $$\dfrac00$$

Finally use $$\sin(A\pm B)$$ formula


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