Question

\(\left(2sin5x-1\right).\left(2cos2x-1\right)=2sinx\)

Answer 1

Với \(cosx=0\) ko phải nghiệm

Với \(cosx\ne0\)

\(\Rightarrow\left(2sin5x-1\right)\left(2cos2x.cosx-cosx\right)=2sinx.cosx\)

\(\Leftrightarrow\left(2sin5x-1\right)\left(cos3x+cosx-cosx\right)=sin2x\)

\(\Leftrightarrow cos3x\left(2sin5x-1\right)=sin2x\)

\(\Leftrightarrow2sin5x.cos3x-cos3x=sin2x\)

\(\Leftrightarrow sin8x+sin2x-cos3x=sin2x\)

\(\Leftrightarrow sin8x=cos3x=sin\left(\dfrac{\pi}{2}-3x\right)\)

\(\Leftrightarrow...\)