Question

sin4x-sin2x=2cos3xsin5x help

Answer 1

$sin(4x)-sin(2x)=2cos(3x)sin(5x)\\ \\ \bigg [ sin(4x)-sin(2x)=2sin(\frac{4x-2x}{2})*\\*cos(\frac{4x+2x}{2})=2sin(x)cos(3x) \bigg ] \\ \\ 2sin(x)cos(3x)-2cos(3x)sin(5x)=0\\ cos(3x)(sin(x)-sin(5x))=0\\ -cos(3x)(-sin(x)+sin(5x))=0\\ cos(3x)(sin(5x)-sin(x))=0\\ cos(3x)*2sin(2x)cos(3x)=0\\ cos^2(3x)*sin(2x)=0\\ \left [ \begin{gathered} cos(3x)=0\\ sin(2x)=0 \end{gathered}\right.$

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