Question

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

Answer 1

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

Answer 2

π/4<a<3π/4
sina>0
sina=√(1-cos^2a)=12/13
0<b<π/4
cosb>0
cosb=√(1-sin^2b)=12/13

sin(a+b)=sinacosb+cosasinb
=12/13*12/13+5/13*5/13
=144/169+25/169
=169/169
=1