Question

1/2sin2x-1/3cosx=0 ПРОШУ РЕШИТЕ ДАЮ 50 БАЛЛОВ

Answer 1

$\frac{1}{2} \sin(2x) - \frac{1}{3} \cos(x) = 0 \\ \frac{1}{2} \times 2 \sin(x) \cos(x) - \frac{1}{3} \cos(x) = 0 \\ \cos(x) ( \sin(x) - \frac{1}{3} ) = 0 \\ \left[ \begin{gathered} \cos(x) = 0 \\ \sin(x) - \frac{1}{3} = 0 \end{gathered} \right. \\ \left[ \begin{gathered} x = \frac{\pi}{2} + \pi n \\ \sin(x) = \frac{1}{3} \end{gathered} \right. \\ \left[ \begin{gathered} x = \frac{\pi}{2} + \pi n, \: n,m \in \mathbb Z \\ x = ( - 1) {}^{m} \arcsin( \frac{1}{3} ) + \pi m\end{gathered} \right.$