How do I prove this Triginomerty equasion?

Question

I got this in a math preparation course I'm taking for college. Can you please help me proving this?

$$\frac{\sin2a\cos a-\cos3a\sin a}{2\sin a}=\cos a$$

Thanks!

Answer 1

HINT: Use Werner Formulas

$$2\sin A\cos B=\sin(A+B)+\sin(A-B)$$

and $$2\sin B\cos A=\sin(A+B)-\sin(A-B)$$

N.B. :The problem seems to be wrong : should start with $\sin3a$