8-4

Steps:
1. Algebra
2. Identities which are sin^2 theta + cos^2 theta=1 1+tan^2 theta=sec^2 theta and 1+cot^2 theta=csc^2 theta
3. Algebra
4. Continue to steps till in simplest form

Ex. 1. Cos^2 theta + sin^2 theta
Use the identity sin^2 theta + cos^2 theta=1. So the answer is 1.

2. (cscA-1) (cscA+1)
foil it out which gives you csc^2A + cscA - cscA-1. Then + cscA - cscA cancels out which leaves you with csc^2A-1. Use the identity 1+cot^2 theta=csc^2 theta. So the answe is cot^2A

3. Csc^2x (1- cos^2x)
Use sin^2 theta + cos^2 theta=1 which gives you csc^2x (sin^2x). Change everything to sin and cos which gives you 1/sin^2x(sin^2x). Sin cancels out which gives you 1.