The correct option is E None of the above
Given cos4x+sin4x=2cos(2x+π)cos(2x+π)
⇒(cos2x+sin2x)2−2cos2xsin2x=cos4x+cos2π
⇒1−12sin22x=cos4x+1
⇒−12(1−cos4x2)=cos4x
⇒cos4x=−13
⇒sin4x=2√23
again cos4x=−13
⇒1−2sin22x=−13
sin2x=√23
Hence, none of the given option is correct.