A,B均为锐角,A+B<180°
cosA=1/4
sinA=根号(1-(1/4)^2)=根号15/4
cos(A+B)=-2/3
sin(A+B)=根号(1-(-2/3)^2)=根号5/3
cos(A+B)=cosAcosB-sinAsinB=-2/3
1/4cosB-根号15/4sinB=-2/3.(1)
sin(A+B)=sinAcosB+cosAsinB=根号5/3
根号15/4cosB+1/4sinB=根号5/3.(2)
(2)* 根号15 +(1):
4cosB=(5根号3-2)/3
cosB=(5根号3-2)/12
(2)-(1)* 根号15 :
4sinB=(2根号15+根号5)/3
sinB=(2根号15+根号5)/12