If `x=cosec theta-sin theta` and `y=cosec^(n)theta-sin^(n) theta`, prove that, `(x^(2)+4)((dy)/(dx))^(2)=n^(2)(y^(2)+4)`.

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 x=sec theta-cos theta, y =sec^(n)theta-cos^(n) theta and (x^(2)+4)((dy)/(dx))^(2)=k(y^(2)+4) then the value of k is -

If x= cosec theta -sin theta and y=sec theta-cos theta, then show that x^(2//3)+y^(2//3)=(xy)^(-2//3)

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

If x = sec theta - cos theta, y = sec^n theta - cos^n theta , then show that (x^2 + 4) (dy/dx)^2 = n^2 (y^2 + 4)

If x+a= a(2 cos theta-cos 2 theta) and y= a(2 sin theta- sin 2 theta) ,show that (x^(2)+y^(2)+2ax)^(2)=4a^(2)(x^(2)+y^(2)) .

x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(n^2(y^2+4))/(x^2+4)

If x=2 cos theta-cos 2 theta and y=2 sin theta-sin 2 theta , then the value of (d^(2)y)/(dx^(2)) at theta=(pi)/(2) is -

If:x/a costheta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2

If x = sin theta + cos theta sin 2 theta " and " y = cos theta + sin theta sin 2 theta,"prove that " (x+y)^(2//3) + (x-y)^(2//3) = 2