Write each identity expression in terms of:1. cos theta= a. sin^2theta

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sec^2theta-1
2. tan theta= a. sec theta over sin theta minus sec theta over cosecant theta.

To express the given identity expressions in terms of the corresponding trigonometric functions, we can manipulate the given equation step by step.

1. To express cos theta in terms of sin^2theta, sec^2theta, and 1, we can use the Pythagorean identity:

sin^2theta + cos^2theta = 1

Rearranging this equation, we get:

cos^2theta = 1 - sin^2theta

Now, we can substitute this expression for cos^2theta in the given equation:

cos theta = sin^2theta / (sec^2theta - 1)

2. To express tan theta in terms of sec theta, sin theta, and cosecant theta, we can use the following trigonometric relationships:

sec theta = 1 / cos theta
cosecant theta = 1 / sin theta

Substituting these relations in the given equation, we get:

tan theta = (1 / cos theta) / (sin theta) - (1 / sec theta) / (cosecant theta)

Simplifying further:

tan theta = (1 / cos theta) / (sin theta) - (cos theta) / (sin theta)

tan theta = (1 - cos theta) / (sin theta)

I hope this helps! Let me know if you have any more questions.