Simplify

sin^2x+cos^2x+sec^2x -tan^2x+csc^2x-cot^2x

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To simplify the given expression, we'll use the fundamental trigonometric identities. These identities relate the trigonometric functions of an angle in a right triangle.

1. Start with the given expression:

sin^2x + cos^2x + sec^2x - tan^2x + csc^2x - cot^2x

2. Recall that for any angle x, the Pythagorean identity states that

sin^2x + cos^2x = 1

We can rewrite the expression using this identity:

1 + sec^2x - tan^2x + csc^2x - cot^2x

3. Another crucial identity is the relationship between secant and cosine:

sec^2x = 1 + tan^2x

By substituting this identity into the expression, we get:

1 + (1 + tan^2x) - tan^2x + csc^2x - cot^2x

4. Next, let's look at the relationship between cscant and sine:

csc^2x = 1 + cot^2x

Substituting this identity into the expression, we have:

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

5. Simplify within each parenthesis:

1 + 1 + tan^2x - tan^2x + 1 + cot^2x - cot^2x

6. Combine like terms:

3

Therefore, the simplified form of the given expression is 3.