If `x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=`

If x=e^(-t^(2)), y=tan^(-1)(2t+1) , then (dy)/(dx)=

If x=e^(-t^(2)), y=tan^(-1)(2t+1) , then (dy)/(dx)=

Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)) , then (dy)/(dx) is equal to

The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a hyperbola of eccentricity

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(2t)/(1+t^2),y=(1-t^2)/(1+t^2),t h e nfin d(dy)/(dx)a tt=2.

If x=(2t)/(1+t^2) , y=(1-t^2)/(1+t^2) , then find (dy)/(dx) .

If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2