How do you express cos(15π8)⋅cos(5π3) without using products of trigonometric functions? Trigonometry Trigonometric Identities and Equations Products, Sums, Linear Combinations, and Applications 1 Answer Shwetank Mauria Mar 13, 2016 12cos(11π24)+12cos(5π24) Explanation: As cos(A+B)=cosAcosB−sinAsinB and cos(A−B)=cosAcosB+sinAsinB, adding them gives us cos(A+B)+cos(A−B)=2cosAcosB Hence cosAcosB=12{cos(A+B)+cos(A−B)} and cos(15π8)cos(5π3)=12{cos(15π8+5π3)+cos(15π8−5π3)} = 12{cos(45π+40π24)+cos(45π−40π24)} = 12{cos(85π24)+cos(5π24)} = 12{cos(96π−11π24)+cos(5π24)} = 12{cos(4π−11π24)+cos(5π24)} = 12cos(11π24)+12cos(5π24)} Answer link Related questions How do you use linear combinations to solve trigonometric equations? How do you derive the multiple angles formula? How do you apply trigonometric equations to solve real life problems? How do you use the transformation formulas to go from product to sum and sum to product? What is the sum to product formulas? How do you change 2sin7xcos4x into a sum? How do you solve sin4x+sin2x=0 using the product and sum formulas? How do you use the sum and double angle identities to find sin3x? How do you simplify sin2θ−cos2θ+tan2θ to non-exponential trigonometric functions? How do you simplify sin2θ to non-exponential trigonometric functions? See all questions in Products, Sums, Linear Combinations, and Applications Impact of this question 1740 views around the world You can reuse this answer Creative Commons License