Question

[Quynh Anh]

sin3x(cosx - sin3x) + cos3x(sinx - cos3x)= 0

Answer 1

[Trần Quốc Lộc]

\(sin3x\left(cosx-sin3x\right)+cos3x\left(sinx-cos3x\right)=0\\ \Leftrightarrow sin3x\cdot cosx+cos3x\cdot sinx=sin^23x+cos^23x\\ \Leftrightarrow sin4x=1=sin\frac{\pi}{2}\\ \Leftrightarrow4x=\frac{\pi}{2}+k2\pi\\ \Leftrightarrow x=\frac{\pi}{8}+\frac{k\pi}{2}\)