Given relations are acos3α+3a‌cos‌α‌sin2‌α=m ....(i) asin3α+3acos2α‌sin‌α=n .....(ii) On adding Eq. (i) and (ii) we get (m+n)=acos3α+3a‌cos‌α‌sin2‌α+3acos2α‌sin‌α+asin3α =a(cos‌α+sin‌α)3 Similarly on subtracting Eq. (ii) from Eq (i) we get m m−n=a(cos‌α−sin‌α)3 Now, (m+n)2∕3+(m−n)2∕3 =a2∕3{(cos‌α+sin‌α)2+(cos‌α−sin‌α)2} =a2∕3{2(cos2α+sin2α)}=2a2∕3