Question: 5. Prove the identity: sin (2x) cos(2x = secx sinx COS X Complete the two columns of the table below to demonstrate that this is

5. Prove the identity: sin (2x) cos(2x = secx sinx COS

5. Prove the identity: sin (2x) cos(2x = secx sinx COS X Complete the two columns of the table below to demonstrate that this is an identity. (12 points) Calculation Reason Given on the left side of the sin(2x) cos(2x) original problem sin x COSX 6. Prove the identity: (cos x + cosy) + (sinx - siny} =2+2cos(x + y) Complete the two columns of the table below to demonstrate that this is an identity. (12 points) Calculation Reason Given on the left side of the (cos x + cosy) + (sinx - siny ) original problem 7. Solve these equations: A. Sin ( x+ =)- sin ( x - ) =1 Part 1: 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) sin x cosx = Part 1: 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. tan' x-3tanx +2 = 0 Part 1: Factor the expression in the equation to make it easier to solve. (2 points) Part II: Solve the equation, finding all solutions. (4 points)

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