simplify and write the trigonometric equation in terms of sine and cosine.

tan^2x-sec^2x

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from the main Pythagorean Identity we know

tan^2 x + 1 = sec^2 x

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

To simplify and write the trigonometric equation in terms of sine and cosine, let's first rewrite the given expression using the trigonometric identities.

The identity tan^2𝑥 - sec^2𝑥 = sin^2𝑥/cos^2𝑥 - (1/cos^2𝑥) can be used to simplify the given equation.

Next, simplify the expression by combining the terms:

(sin^2𝑥 - 1)/cos^2𝑥.

Now, we can further rewrite the expression using the trigonometric identity sin^2𝑥 = 1 - cos^2𝑥:

(1 - cos^2𝑥 - 1)/cos^2𝑥.

The two "-1" terms cancel each other out:

-cos^2𝑥/cos^2𝑥.

Finally, we are left with:

-1.

Therefore, the simplified equation, in terms of sine and cosine, is:

-1.