if `y = cosec @ + cottheta `, prove that `2(dy)/(d theta) + y^2 + 1 = 0.`

If y = cosec theta + cot theta , prove that 2(dy)/(d theta)+ y^(2)+ 1 = 0 .

If x =a cot theta , y=b cosec theta ,then (dy)/(dx)=

If x=sectheta - tantheta and y = cosec theta+ cottheta , then prove that xy +1 = y - x.

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

1+cottheta="cosec"theta

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

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+cottheta=p ,then prove that: cos theta=(p^(2)-1)/(p^(2)+1)

If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))^2=3\ s in^2theta(5\ cos^2theta-1) .

If x=sectheta "and " y=cosec theta +cottheta , then prove that xy+1=y-x .