Simplify the expression sin^2x+tan^2x-sec^2x+cos^2x.

We notice that using Pythagorean identity, we can replace
the sum:

(sin x)^2 + (cos x)^2 =
1

The expression will
become:

1 + (tan x)^2 - (sec
x)^2

But 1 + (tan x)^2 = 1/(cos
x)^2

We also know that 1/(cos x)^2 = (sec
x)^2

We'll re-write the
expression:

1 + (tan x)^2 - (sec x)^2 = (sec x)^2 - (sec
x)^2 = 0

We notice that simplifying the
expression, we'll get the result: (sin x)^2 + (cos x)^2 + (tan x)^2 - (sec x)^2 =
0.