### Home > PC3 > Chapter 8 > Lesson 8.3.3 > Problem 8-115

8-115.

Simplify each the following trigonometric expressions. Homework Help ✎

cos(

*A*)cot(*A*) + sin(*A*)sin

^{2}(*θ*) + tan^{2}(*θ*) – cot^{2}(*θ*) + cos^{2}(*θ*) – sec^{2}(*θ*) + csc^{2}(*θ*)

1. Rewrite everything in terms of sine and cosine.

2. Get a common denominator.

3. Use the Fundamental Pythagorean Identity.

4. Simplify.

Use the Pythagorean Identities.

Change their forms to get 1s.

cos^{2}(*θ*) + sin^{2}(*θ*) = 1

1 + tan^{2}(*θ*) = sec^{2}(*θ*)

1 + cot^{2}(*θ*) = csc^{2}(*θ*)