[" EXANIPLE "15" If "a cos^(3)x+3a cos x sin^(2)x=m" and "a sin^(3)x+3a cos^(2)x sin x=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 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 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 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 alpha=m and a sin^(3)alpha+3a cos^(3)alpha sin^(3)alpha=n then (m+n)^((2)/(3))+(m-n)^((2)/(3))

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 +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^(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 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 x cos A + y sin A = m and x sin A - y cos A = n, then prove that : x^(2) + y^(2) = m^(2) + n^(2)