\(A=\dfrac{1}{2}sin4x-\dfrac{1}{2}sin2x+\dfrac{1}{2}sin12x+\dfrac{1}{2}sin2x\)
\(=\dfrac{1}{2}sin4x+\dfrac{1}{2}sin12x=sin8x.cos4x\)
\(B=\dfrac{1}{2}cos5x+\dfrac{1}{2}cos3x+\dfrac{1}{2}cosx-\dfrac{1}{2}cos5x\)
\(=\dfrac{1}{2}cos3x+\dfrac{1}{2}cosx=cos2x.cosx\)