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# 9.4E: Sum-to-Product and Product-to-Sum Formulas (Exercises)

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For the following exercises, evaluate the product for the given expression using a sum or difference of two functions. Write the exact answer.

30. $$\cos \left(\frac{\pi}{3}\right) \sin \left(\frac{\pi}{4}\right)$$

31. $$2 \sin \left(\frac{2 \pi}{3}\right) \sin \left(\frac{5 \pi}{6}\right)$$

32. $$2 \cos \left(\frac{\pi}{5}\right) \cos \left(\frac{\pi}{3}\right)$$

For the following exercises, evaluate the sum by using a product formula. Write the exact answer.

33. $$\sin \left(\frac{\pi}{12}\right)-\sin \left(\frac{7 \pi}{12}\right)$$

34. $$\cos \left(\frac{5 \pi}{12}\right)+\cos \left(\frac{7 \pi}{12}\right)$$

For the following exercises, change the functions from a product to a sum or a sum to a product.

35. $$\sin (9 x) \cos (3 x)$$

36. $$\cos (7 x) \cos (12 x)$$

37. $$\sin (11 x)+\sin (2 x)$$

38. $$\cos (6 x)+\cos (5 x)$$