Find the general formula of sin 2A = cos 3A

 sin2A = sin(90-3A)

$$\begin{gathered} 2A = 2n\mathrm{\pi } \pm (\frac{\mathrm{\pi }}{2}-3\mathrm{A}) \\ \mathrm{So} \mathrm{taking} \mathrm{positive} \mathrm{sign} , \mathrm{we} \mathrm{have} \\ 5\mathrm{A} = 2\mathrm{n\pi } +\frac{\mathrm{\pi }}{2} \\ \mathrm{Or} \mathrm{A} =\frac{2\mathrm{n\pi }}{5} +\frac{\mathrm{\pi }}{10} \\ \mathrm{And} \mathrm{taking} \mathrm{negative} \mathrm{sign} , \mathrm{we} \mathrm{have} \\ 2\mathrm{A} = 2\mathrm{n}\mathrm{\pi } - (\frac{\mathrm{\pi }}{2}-3\mathrm{A}) \\ 2\mathrm{A} = 2\mathrm{n\pi }-\frac{\mathrm{\pi }}{2} +3\mathrm{A} \\ \frac{\mathrm{\pi }}{2} -2\mathrm{n\pi } = \mathrm{A} \end{gathered}$$