what are the steps to vertifying this
1+sec^2x(sin^2x)=sec^2x

You can convert the secant function to its cosine equivalent, and it comes right out. Or alternatively - divide the equation through by sec^2x and it becomes apparent.

(1-tan^2x)^2=sec^4x-4tan^2x

As usual - convert tangenat and secant functions to sine and cosine equivalents, then simplify.