Question

giải phương trình:

cos³x.sin3x + sin³x.cos3x = sin³4x

Answer 1

\(\Leftrightarrow\left(3cosx+cos3x\right)sin3x+\left(3sinx-sin3x\right)cos3x=4sin^34x\)

\(\Leftrightarrow3\left(sin3x.cosx+cos3x.sinx\right)=4sin^34x\)

\(\Leftrightarrow3sin4x=4sin^34x\)

\(\Leftrightarrow sin4x\left(3-4sin^24x\right)=0\)

\(\Leftrightarrow sin4x\left(1+2cos8x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sin4x=0\\cos8x=-\frac{1}{2}\end{matrix}\right.\) \(\Leftrightarrow...\)