Question

若cosα*cosβ=1,则sin(α+β)=

Answer 1

cosα*cosβ=1
cosα =cosβ=1 此时sinα=0，cosβ=0
或
cosα=cosβ=-1， 此时sinα=0，cosβ=0
sin(α+β)=sinαcosβ+cosαsinβ)=0+0=0

Answer 2

cosα*cosβ=1
(cosα) = 1/cosβ
|1/cosβ| <=1
=>cosα = 1 or -1
when cosα =1, cosβ =1, sinα=0, cosβ =0
when cosα =-1, cosβ =-1, sinα=0, cosβ =0

case 1: cosα =1, cosβ =1, sinα=0, cosβ =0
sin(α+β) = sinαcosβ + cosαsinβ
=0
case 2: cosα =-1, cosβ =-1, sinα=0, cosβ =0
sin(α+β) = sinαcosβ + cosαsinβ
=0

ie
sin(α+β) =0