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If the dependent variable y is changed ...

If the dependent variable `y` is changed to `z` by the substitution `y=tanz` and the differential equation `(d^2y)/(dx^2)=1+(2(1+y))/(1+y^2)((dy)/(dx))^2` is changed to `(d^2z)/(dx^2)=cos^2z+k((dz)/(dx))^2,` then the value of `k` equal to_______

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