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

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 x=sec theta-tan theta and y=cos ec theta+cot theta then prove that xy+1=y-x

If cot theta+tan theta=x and sec theta-cos theta=y prove that (x^(2)y)^((2)/(3))-(xy^(2))^((2)/(3))=1

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

if cot theta+tan theta=x and sec theta-cos theta=y, prove that (x^(2)y)^((2)/(3))-(xy^(2))^((2)/(3))=1

If x=sec theta-tan theta and y="cosec"theta+cot theta," then " y-x-xy=

If x=sec theta-tan theta and y="cosec"theta+cot theta," then " y-x-xy=

If x=sec theta - tan theta, y = cosec theta + cot theta then prove that xy+x-y+1=0 .

If cosec theta- sin theta= a^3, sec theta- cos theta= b^3 , prove that a^2b^2(a^2+b^2)=1 .

If 2cos theta-sin theta=x and cos theta-3sin theta=y Prove that 2x^(2)+y^(2)-2xy=5