If `a cos^3 alpha +3acosalpha*sin alpha = m` and `a sin^3alpha +3a cos^3alpha sin^3alpha = n` then`(m + n)^(2/3) + (m-n)^(2/3)`

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=m and a sin^(2)alpha+3a cos^(2)alpha sin alpha=n then (m+n)^((2)/(3))+(m-n)^((2)/(3))=

If acos^3alpha+3acosalphasin^2alpha=m and asin^3alpha+3acos^2alphasinalpha=n then (m+n)^(2/3)+(m-n)^(2/3)=

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=ma sin^(3)alpha+3a cos^(2)alpha sin alpha=n, then (m+n)^((2)/(3))+(m-n)^((2)/(3))=

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=m and a sin^(3)alpha+3a cos^(2)alpha sin alpha=n. If (m+n)^((2)/(3))+(m-n)^((2)/(3))=2 lambda a^((2)/(3)) then find the value of lambda

If acos^(3)alpha+3cosalphasin^(2)alpha=m and asin^(3)alpha+3cos^(2)alphasinalpha=n , then (m+n)^(2//3)+(m-n)^(2//3)=?

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

(cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3 alpha )/( sin alpha ) = 3.

If x sin ^ (3) alpha + y cos ^ (3) alpha = sin alpha cos alpha and x sin alpha-y cos alpha = 0 then x ^ (2) + y ^ (2) =