三角函数计算2

(sinα+sinβ)^2=(sinα)^2+(sinβ)^2+2sinαsinβ=1/16
(cosα+cosβ)^2=(cosα)^2+(cosβ)^2+2cosαcosβ=1/9
上两式相加得1+1+2（cosαcosβ+sinαsinβ）=25/144
cosαcosβ+sinαsinβ=-263/288=cos(α-β)
上两式相减得
cos2α+cos2β+2cos(α+β)=1/9-1/16=7/144
2cos(α+β)cos(α-β)+2cos(α+β)=7/144
cos(α+β)[1+cos(α-β)]=7/288
cos(α+β)(1+263/288)=7/288
cos(α+β)=7/551
sin(α+β)=根号(1-49/303601)=(根号303552)/551=根号527*24/551

tan(α+β)
=sin(α+β)/cos(α+β)
=根号527*24/7

3/4

2/3

24/7

(sinα+sinβ)^2=(sinα)^2+(sinβ)^2+2sinαsinβ=1/16
(cosα+cosβ)^2=(cosα)^2+(cosβ)^2+2cosαcosβ=1/9
上两式相加得1+1+2（cosαcosβ+sinαsinβ）=25/144
cosαcosβ+sinαsinβ=-263/288=cos(α-β)
上两式相减得
cos2α+cos2β+2cos(α+β)=1/9-1/16=7/144
2cos(α+β)cos(α-β)+2cos(α+β)=7/144
cos(α+β)[1+cos(α-β)]=7/288
cos(α+β)(1-263/288)=7/288
cos(α+β)=7/25
sin(α+β)=根号(1-49/625)= 24/25
tan(α+β)=sin(α+β)/cos(α+β) = 24/7