a=(√3sin2x,cos2x),b=(cos2x,-cos2x)
a●b=√3sin2xcos2x-cos²2x
=√3/2*sin4x-1/2(1+cos4x)
=√3/2sin4x-1/2*cos4x-1/2
=sin(4x-π/6)-1/2
∵a●b+1/2=-3/5
∴sin(4x-π/6)=-3/5
∵x∈(7π/24,5π/12)
∴4x∈(7π/6,5π/3)
∴4x-π/6∈(π,3π/2)
∴cos(4x-π/6)=-4/5
∴cos4x
a=(√3sin2x,cos2x),b=(cos2x,-cos2x)
a●b=√3sin2xcos2x-cos²2x
=√3/2*sin4x-1/2(1+cos4x)
=√3/2sin4x-1/2*cos4x-1/2
=sin(4x-π/6)-1/2
∵a●b+1/2=-3/5
∴sin(4x-π/6)=-3/5
∵x∈(7π/24,5π/12)
∴4x∈(7π/6,5π/3)
∴4x-π/6∈(π,3π/2)
∴cos(4x-π/6)=-4/5
∴cos4x