\(A=\dfrac{1}{2}cosa\left[cos\left(b+c\right)+cos\left(b-c\right)\right]\)
\(=\dfrac{1}{2}cosa.cos\left(b+c\right)+\dfrac{1}{2}cosa.cos\left(b-c\right)\)
\(=\dfrac{1}{4}cos\left(a+b+c\right)+\dfrac{1}{4}cos\left(a-b-c\right)+\dfrac{1}{4}cos\left(a+b-c\right)+\dfrac{1}{4}cos\left(a-b+c\right)\)
\(B=\dfrac{1}{2}sin2a\left(cos2a-cos10a\right)=\dfrac{1}{2}sin2a.cos2a-\dfrac{1}{2}sin2a.cos10a\)
\(=\dfrac{1}{4}sin4a-\dfrac{1}{4}sin12a+\dfrac{1}{4}sin8a\)
\(C=\dfrac{1}{2}\left(cos\dfrac{\pi}{3}-cos2x\right)cos2x=\dfrac{1}{2}cos2x\left(\dfrac{1}{2}-cos2x\right)\)
\(=\dfrac{1}{4}cos2x-\dfrac{1}{2}cos^22x=\dfrac{1}{4}cos2x-\dfrac{1}{2}\left(\dfrac{1}{2}+\dfrac{1}{2}cos4x\right)\)
\(=\dfrac{1}{4}cos2x-\dfrac{1}{4}cos4x-\dfrac{1}{4}\)
