1、(sinα)^2+(sinβ)^2+2sinαsinβ=m^2,(1)
(cosα)^2+(cosβ)^2+2cosαcosβ=n^2,(2)
(1)+(2),
1+1+2cos(α-β)=m^2+n^2,
cos(α-β)=(m^2+n^2)/2-1.
2、tanx+cotx= sinx/cosx+cosx/sinx=1/(sinxcosx),
sinx+cosx=1/2,
1+2sinxcosx=1/4,
sinxcosx=-3/8,
tanx+cotx=-8/3.
3、sin(α+β）=1/2,
sinαcosβ+cosαsinβ=1/2,(1)
sinαcosβ-cosαsinβ=1/3,(2)
(1)+(2),
2sinαcosβ=5/6,
sinαcosβ=5/12,(3)
(1)-(2),
cosαsinβ=1/12,(4)
(3)/(4)
tanαcotβ=5.
4、tanx=1/cotx=1/2,
tan(y-x)=-tan(x-y)=2/5,
tany=tan(y-x+x)=[tan(y-x)+tanx]/[1-tan(y-x)tanx]
=(2/5+1/2)/(1-1/5)
=9/8.
5、cosα=1/3,cos（α+β）=-3/5,
α 、β是锐角,α+β