[TEX]\begin{array}{l}\sin ^5 x - c{\rm{os}}^5 x = - 1 \\ \Leftrightarrow \sin ^5 x - c{\rm{os}}^5 x + \sin ^2 x + c{\rm{os}}^2 x = 0 \\ \Leftrightarrow \sin ^2 x\left({\sin ^3 x + 1} \right) + c{\rm{os}}^2 x\left( {1 - c{\rm{os}}^3 x} \right) = 0 \\ \Leftrightarrow \left\{ \begin{array}{l} \sin ^2 x\left( {\sin ^3 x + 1} \right) = 0 \\ c{\rm{os}}^2 x\left( {1 - c{\rm{os}}^3 x} \right) = 0 \\ \end{array} \right. \\\Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} \sin x = 0 \\ \cos x = 1 \\ \end{array} \right. \\ \left\{ \begin{array}{l} \sin x = - 1 \\ \cos x = 0 \\\end{array} \right. \\ \end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = k2\pi \\ x = \frac{{ - \pi }}{2} + k2\pi \\ \end{array} \right. \\ \end{array}[/TEX]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
