Mathematics - Lecture 24 "Half measure identities, product-to-sum and sum-to-product identities" presents the following content: Half measure identities, product-to-sum and sum-to-product identities. | Half Measure Identities, Product-to-Sum and Sum-to-Product Identities Institute of Mathematics, University of the Philippines Lecture 24 (IMath, UP) Other Identities Lec. 24 1 / 21 1 Half Measure Identities 2 Product-to-Sum and Sum-to-Product Identities (IMath, UP) Other Identities Lec. 24 2 / 21 Recall: cos 2θ = 2 cos2 θ − 1 (IMath, UP) Other Identities Lec. 24 3 / 21 Recall: cos 2θ = 2 cos2 θ − 1 θ Replace θ by 2 : (IMath, UP) Other Identities Lec. 24 3 / 21 Recall: cos 2θ = 2 cos2 θ − 1 θ Replace θ by 2 : θ θ cos(2 · 2 ) = 2 cos2 ( 2 ) − 1 (IMath, UP) Other Identities Lec. 24 3 / .