cos3x = sinx ⟺ cos3x = cos\(\left( {\frac{\pi }{4} - x} \right)\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{3x = \frac{\pi }{2} - x + k2\pi }\\{3x = - \frac{\pi }{2} + x + k2\pi }\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{4x = \frac{\pi }{2} + k2\pi }\\{2x = - \frac{\pi }{2} + k2\pi }\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{\pi }{8} + \frac{{k\pi }}{2}}\\{x = - \frac{\pi }{4} + k\pi }\end{array}} \right.\,\left( {k \in \mathbb{Z}} \right)\)

+) \(0 < \frac{\pi }{8} + \frac{{k\pi }}{2} < \pi \Rightarrow - \frac{1}{4} < k < \frac{7}{4} \Rightarrow k = 0.1 \Rightarrow x = \frac{\pi }{8};x = \frac{{5\pi }}{8}\)

+) \(0 < - \frac{\pi }{4} + k\pi < \pi \Rightarrow \frac{1}{4} < k < \frac{5}{4} \Rightarrow k = 1 \Rightarrow x = \frac{{3\pi }}{4}\)

⇒ Có 3 nghiệm.