Giải phương trình: sin2x – cos3x = 0

sin2x – cos3x = 0

⇔\(\cos \left( {2x - \frac{\pi }{2}} \right) - \cos 3x = 0\)

⇔\( - 2\sin \left( {\frac{{5x}}{2} - \frac{\pi }{4}} \right).\sin \left( { - \frac{x}{2} - \frac{\pi }{4}} \right) = 0\)

⇔\(\left[ \begin{array}{l}\sin \left( {\frac{{5x}}{2} - \frac{\pi }{4}} \right) = 0\\\sin \left( {\frac{x}{2} + \frac{\pi }{4}} \right) = 0\end{array} \right.\)

⇔\[\left[ \begin{array}{l}\frac{{5x}}{2} - \frac{\pi }{4} = k\pi \\\frac{x}{2} + \frac{\pi }{4} = k\pi \end{array} \right.\]

⇔\[\left[ \begin{array}{l}x = \frac{\pi }{{10}} + \frac{{k2\pi }}{5}\\x = - \frac{\pi }{2} + k2\pi \end{array} \right.\,\left( {k \in \mathbb{Z}} \right)\].