题源展示1.《人教A版新课标实验教材数学必修4》习题3.2A组第4题已知x+y=2~(1/2)sin(θ+π/4),x-y=2~(1/2)sin(θ-π/4),求证:x~2+y~2=1.2.复习参考题B组第8题已知sinβ+cosβ=1/5,β(0,π).(1)求tanβ的值;(2)你能根据所给的条件,自己够造出一些求值的命题吗?题源分析1题:将已知两式相加即求x、y,本题易证;将已知两式平方相加即证本题。此题揭示sinθ+cosθ,sinθ-cosθ两个对偶式的联系,并为三角代换提供的思维空间. Source of the show 1. “People teach A version of the new curriculum standard textbook compulsory math 4” Exercise 3.2A group of the fourth problem is known x + y = 2 ~ (1/2) sin (θ + π / 4), xy = 2 ~ (1/2) sin (θ-π / 4), verify that: x ~ 2 + y ~ 2 = 1.2. π). (1) Seeking the value of tanβ; (2) Can you make some propositions for yourself according to the given conditions? Problem Analysis 1 Problem: y, the title easy card; the sum of two squares known to prove that the problem. This issue reveals the sinθ + cosθ, sinθ-cosθ two dual connections, and provide the thinking space for the triangular substitution.