已知π/4小于4分之3π,0小于β小于π/4,cosα=5/13,sinβ=5/13,求sinα+β

题目

已知π/4小于4分之3π,0小于β小于π/4,cosα=5/13,sinβ=5/13,求sinα+β

答案

π/4＜α＜3π/4
cosα=5/13
sinα=根号(1-cos^2α)=12/13
0＜β＜π/4
sinβ=5/13
cosβ=根号(1-sin^2β)=12/13
sin(α+β)=sinαcosβ+cosαcosβ
= 12/13 * 12/13 + 5/13 * 5/13
= 1