Simplify: (2(1-cos^2x))/(1-sin^2x)

`(2(1-cos^2x))/(1-sin^2x)`

To simplify this, apply the Pythagorean identity  `sin^2x + cos^2x=1` .

`= (2*sin^2x)/(cos^2x)`

And, apply the formula  `tan x = (sinx)/(cosx)` .

`= 2 * ((sinx)/(cosx))^2`

`=2*tan^2x`

`=2tan^2x`

Therefore, the simplified form is `(2(1-sin^2x))/(1-cos^2x)=2tan^2x` .