[" 34.If "x=cosec A+cos A" and "y=cosec A-cos A" then prove that "],[qquad ((2)/(x+y))^(2)+((x-y)/(2))^(2)-1=0]

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

x=a cosec theta+b cot theta, y=a cosec theta-b cot theta . Then, ((x+y)/(a))^(2)-((x-y)/(b))^(2)=4

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 y=("cosec "x+cotx) , prove that (sinx)(d^(2)y)/(dx^(2))-y^(2)=0.

If y=cosec x+cot x show that sin x*(d^(2)y)/(dx^(2))=y^(2)

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 y = cosec^-1x,x>1 , then show that : x(x^2-1)(d^2y)/(dx^2) + (2x^2-1)(dy)/(dx) = 0

If y=csc^(-1)x,x>1, then show that x(x^(2)-1)(d^(2)y)/(dx^(2))+(2x^(2)-1)(dy)/(dx)=0