s(a+b)-s(a-b)=2c(a)s(b) ∴c(a)s(b)=(1/2)(s(a+b)-s(a-b)) This can be written as s(b)c(a)=(1/2)(s(b+a)+s(b-a)) (∵-s(α)=s(-α)) which is essentially same as Identity 3.
These "product to sum" identities c(a)c(b)=(1/2)(c(a+b)+c(a-b)) s(a)s(b)=-(1/2)(c(a+b)-c(a-b)) s(a)c(b)=(1/2)(s(a+b)+s(a-b)) c(a)s(b)=(1/2)(s(a+b)-s(a-b)) are often used to integrate products of trigonometric functions.
Let M=a+b, N=a-b and we obtain the "sum to product" identities c(M)+c(N)=2c((M+N)/2)c((M-N)/2) c(M)-c(N)=-2s((M+N)/2)s((M-N)/2) s(M)+s(N)=2s((M+N)/2)c((M-N)/2) s(M)-s(N)=2c((M+N)/2)s((M-N)/2) which are, in contrast, seldom used. 0650132人目の素数さん2017/12/25(月) 05:20:38.79ID:bCeVd4// 偽増田も居なくなったね 0651memo2017/12/30(土) 04:01:22.26ID:4hq5CwJF Hadamard defined that a problem is "well-posed" when one and only solution exists, and the solution isn't sensitive to the change in the initial condition. Existance, uniqueness, and stability of the solution is important in mathematical analysis.
Consider the following problem; find a_n where a_1=2, a_2=4, a_3=8. a_n=2^n may be the standard answer, but a_n=n^2-n+2 also satisfies the given condition. Having two (or perhaps more) valid answers means that this problem is "ill-posed." Oddly enough, this type of problem (finding the general term of a sequence from several given terms) is common in highschool math tests. 0652memo2017/12/30(土) 04:12:15.39ID:4hq5CwJF typos Existance -> Existence highschool -> high school 0653132人目の素数さん2017/12/31(日) 23:38:45.64ID:iR/S/9ug 今まで読んだ中で一番難しかった 論文は何? 0654132人目の素数さん2018/01/07(日) 20:01:02.94ID:UzDi6Kuq 成績いいからって医学科来るな https://anond.hatelabo.jp/201801052241470655¥ ◆2VB8wsVUoo 2018/01/19(金) 21:29:11.68ID:ujRq+81i ¥ 0656¥ ◆2VB8wsVUoo 2018/01/19(金) 21:29:33.07ID:ujRq+81i ¥ 0657¥ ◆2VB8wsVUoo 2018/01/19(金) 21:29:52.55ID:ujRq+81i ¥ 0658¥ ◆2VB8wsVUoo 2018/01/19(金) 21:30:14.71ID:ujRq+81i ¥ 0659¥ ◆2VB8wsVUoo 2018/01/19(金) 21:30:33.42ID:ujRq+81i ¥ 0660¥ ◆2VB8wsVUoo 2018/01/19(金) 21:30:53.11ID:ujRq+81i ¥ 0661¥ ◆2VB8wsVUoo 2018/01/19(金) 21:31:10.38ID:ujRq+81i ¥