5. Prove the identity: Part I: Complete the left-hand column of the table below following the steps indicated in the right-hand column. (12 points)
Calculation Reason

Given on the left side of the original problem

Apply the double-angle formulas for sine and cosine

Simplify the expression

Definition of secant

6. Prove the identity:

Part I: Complete the left-hand column of the table below following the steps indicated in the right-hand column. (12 points)
Calculation Reason

Given on the left side of the original problem

Expand each squared term

Simplify the expression

Apply the Pythagorean identity

Apply the addition formula for cosine

7. Solve these equations:
A.

Part I:
Apply the sum and difference formulas for sine to simplify the left-hand side of the equation. (2 points)

Part II:
Find all solutions to the equation you found in part I. (4 points)

B.

Part I:
Use the double-angle formula for sine to rewrite the problem in terms of sine only. (2 points)

Part II:
Solve the equation, finding all solutions. (4 points)

C.

Part I:
Factor the expression in the equation to make it easier to solve. (2 points)

Part II:
Solve the equation, finding all solutions. (4 points)