Question

已知sin(α+β)=1则sin(2α+β)+sin(2α+3β)=?

Answer 1

sin(α+β)=1 α+β=π/2
sin(2α+β)+sin(2α+3β)=sin(α+π/2)+sin(3π/2-α)=cosα－cosα=0

Answer 2

解：因为sin(α+β)=1
所以α+β=0所以α=-β
所以sin(2α+β)+sin(2α+3β)=sin(α)+sin(β)=sin(α)+sin(-α)=sin(α)-sin(α)=0