In which of the following sets the inequality sin6⁡x+cos6⁡x>5/8 holds good?

sin2⁡x+cos2⁡x3−3sin2⁡xcos2⁡x×sin2⁡x+cos2⁡x>58 or  1−3sin2⁡xcos2⁡x>58 or  38>3sin2⁡xcos2⁡x⇒ 1−2sin2⁡2x>0⇒ cos⁡4x>0⇒ 4x∈−π2,π2⇒ 4x∈2nπ−π2,2nπ+π2n∈Z generalizing now verify.