If `acos^2theta+3acosthetas in^2theta=ma n das in^3theta+3acos^2thetas in^theta=n` , then prove that: `(m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)`

If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasintheta=n , then prove that: (m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)

If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasin^theta=n , then prove that: (m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)

If a cos^(2)theta+3a cos theta sin^(2)theta=m and a sin^(3)theta+3a cos^(2)theta sin theta=n ,then prove that: (m+n)^(2/3)+(m-n)^(2/3)=2a^(2/3)

If c cos^(3)theta+3c cos theta sin^(2)theta=m and c sin^(3)theta+3c cos^(2)theta sin theta=n , then prove that (m+n)^((2)/(3))+(m-n)^((2)/(3))=2c^((2)/(3)).

If m= a Cos^(3) theta + 3a Cos theta Sin^(2) theta and n=a Sin^(3) theta + 3 a Cos^(2) theta Sin theta then (m+n)^(2//3) + (m-n)^(2//3) =

If " cosec"theta-sin theta=m and sec theta-cos theta=n , then prove that (m^(2)n)^((2)/(3))+(mn^(2))^((2)/(3))=1.

If cos ec theta - sin theta = m and sec theta - cos theta = n, then show that (m ^(2) n ) ^(2//3) + (mn ^(2)) ^( 2//3) = 1.

If cosec theta- sin theta = m and sec theta - cos theta = n , prove that: (m^(2)n)^(2/3)+(n^(2)m)^(2/3)=1 .

If acos theta+bsintheta =m and asin theta-bcostheta =n, prove that m^(2)+n^(2)=a^(2)+b^(2)