If `sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6,)` w h e r e-1x,1a n d-1

Explanation

`sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3)`

let`x^3=sintheta` and `y^3=sin phi`

`costheta+cosphi=a^3(sintheta-sinphi)`

=`2acos((theta+phi)/2)cos((theta-phi)/2)=a^32acos((theta+phi)/2)sin((theta-phi)/2)`

`(theta-phi)/2=cot^(-1)a^3`


`(theta-phi)=2cot^(-1)a^3`

=`sin^(-1)x^3-sin^(-1)y^3=2cot^(-1)a^3`

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