1. Simplify the given expression: sec²t csct csc²t sect

2. Simplify the giving expression: (sinx + cosx)(sinx – cosx) + 1 sin²x

3. Prove the identity: Sin t = 1 + cost 1-cost sint

4. Prove the identity: (sinx + cosx)² - sin2x = 1

5. Prove the identity: tanx + cotx = secxcscx

6. Prove the identity: (1-cos²x)cscx = sinx

7. Prove the identity: 1 + secx = cscx tanx + sinx

8. Using an addition or subtraction identity find the exact value of: Cos 7 π/12

9. Using an addition or subtraction identity, find the exact value of the following: Sin π/12

10. Rewrite the following in terms of sin x and cos x. (hint: use addition or subtraction identity) Sin ( π/2 +x)

11. Simplify the given expression: Cos(x+y) – cos(x-y)

12. If x is in Q1 and y is in Q2, sinx = 24/25, and siny =4/5 find the exact value of sin(x+y) and tan(x+y).

13. Use the half angle identities to solve the following: Cos 7 π/8

14. Use the half angle identities to solve: Tan 5 π/8

15. Write each as a sum or difference: cos2xcos4x

16. Write each expression as a product: Sin9x – sin5x

17. For the given, find the sin2x, cos2x, tan2x Cos x = -⅓ for π/2 < x < π