已知13sinα+5cosβ=9,平方得 169sin^2α+2*13*5sinαcosβ+25cos^2β=81
13cosα+5sinβ=15,169cos^2α+2*13*5sinβcosα+25sin^2β=225
相加
169+25+130（sinαcosβ+sinβcosα）=306
sinαcosβ+sinβcosα=56/65
sinαcosβ+sinβcosα=sin(α+β)=56/65
2.
cosβ=cos[(α+β)-a]=cos(α+β)cosa+sin(α+β)sina
y=(-3/5)*√(1-x^2)+4/5x
sinα=x,α,β∈(0,π/2),定义域x∈(0,1)
3.
sinβ=sin[(a+β)-a]=sin(a+β)cosa-cos(a+β)sina
sin(2α+β)=sin[(a+β)+a]=sin(a+β)cosa+cos(a+β)sina
sinβ=msin(2α+β)
sin(a+β)cosa-cos(a+β)sina=msin(a+β)cosa+mcos(a+β)sina
(1-m)sin(a+β)cosa=(1+m)cos(a+β)sina
sin(a+β)/cos(a+β)=[sina/cosa][(1+m)/(1-m)]
tan(α+β)=(1+m/1-m)tanα