if `x=secA+sinAandy=secA-sinA ,p r o v e t h a t(2/(x+y))^2+((x-y)/2)^2=1`

If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-(x^2+y^2)/(y^3)

If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

If 2x=secA and (2)/(x)=tanA, " prove that " (x^(2)-(1)/(x^(2)))=(1)/(4).

If y=sin^(-1)x , \ s how \ t h a t \ (d^2y)/(dx^2)=x/((1-x^2)^(3/2))

If x=sin theta,y=cosptheta,p rov e \ t h a t (1-x^2)y_2-x y_1+p^2y=0,w h e r e \ y_2=(d^2y)/(dx^2) \ a n d \ y_1=(dy)/(dx)

If x ylog(x+y)=1,p rov e \ t h a t \ (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y))dot

If y=(xsin^(-1)x)/(sqrt(1-x^2)),"p r o v et h a t"(1-x^2)(dy)/(dx)=x+y/xdot

If 2x=secA and (2)/(x)=tanA , then the value of 2(x^(2)-(1)/(x^(2))) is equal to