Question

若sinβ=1/3,sin(α+β)=1,则sin(2α+β)=?

详细步骤

Answer 1

sin(2a+b)=sin[(a+b)+a]=sin(a+b)cosa+cos(a+b)sina
,因为sin(a+b)=1
所以,cos(a+b)=0,
所以sin(2a+b)=cosa,
又因为sin(a+b)=1
所以a+b=2kπ+π/2,
所以cosa=cos(2kπ+π/2-b)=cos(π/2-b)=sinb=1/3.

Answer 2

sin(α+β)=1 α+β=2kπ+π/2 α=2kπ+π/2-β
sin(2α+β)=cosα=cos(2kπ+π/2-β)= cos(π/2-β)=sinβ=-1/3