Check (I): LHS =1−sin6α=(1−sin2α)(1+sin2α+sin4α) ⇒=cos2α(1+(1−cos2α)+(1−cos2α)2) ⇒=cos2α(3−3cos2α+cos4α) ⇒ RHS ✔ So, (I) is true. Check (II): LHS =cos8α−sin8α=(cos4α−sin4α)(cos4α+sin4α) ⇒(cos2α−sin2α)(cos2α+sin2α)(cos4α+sin4α) ⇒(cos2α)(1)(cos4α+sin4α) RHS =2sin2α(1−cos4α+sin2αcos2α) This form does not simplify to LHS. So, (II) is false.
