The correct options are
A 2
B 0
C a∈[−2,2]
D −2
Given equation 4sin(x+π3)cos(x−π6)=a2+√3sin2x−cos2x
4[sinxcosπ3+cosxsinπ3]×[cosxcosπ6+sinxsinπ6]=a2+√3sin2x−cos2x
⇒4[12sinx+√32cosx][√32cosx+12sinx]=a2+√3sin2x−cos2x
⇒√3sin2x+3cos2x+sin2x=a2+√3sin2x−cos2x
⇒cos2x+2=a2−cos2x
⇒cos2x=a2−22
⇒−1≤a2−22≤1
⇒0≤a2≤4
⇒−2≤a≤2.
all values of a given in (a), (b), (c), (d) satisfy this relation.