Question

(1-sin^2(x))tan(-x) is not equivalent

Answer 1

We can simplify (1 - sin^2 (x)) tan(-x) as
-cos^2 (x). sin(x)/cos(x) = -cos(x) sin(x)
Since sin^2 (x) + cos^2 (x) = 1 and tan (-x) = -tan (x). (It may also be useful to know that cot (-x) = -cot(x) which will be incorporated in my solution later)