已知SINA+SINB=3/5,COSA+COSB=4/5,求COS(A-B),SIN(A+B)+COS(A+B)

(sinA+sinB)(sinA+sinB)＝1+2sinAsinB=9／25
sinAsinB=-8/25
(cosA+cosB)(cosA+cosB)=1+2cosAcosB=16/25
cosAcosB=-9/50
cos(A-B)=cosAcosB+sinAsinB=-1/2
SIN(A+B)+COS(A+B)=或者＝根号2倍的cos(A+B-45度）＝根号2倍的[cos(A+B)cos45度+sin(A+B)sin45]
=1/2[cos(A+B)+sin(A+B)]
=2分之根号2倍的cos0
=2分之根号2
（本人是高一的这块刚讲）

(sinA+sinB)(sinA+sinB)＝1+2sinAsinB=9／25
sinAsinB=-8/25
(cosA+cosB)(cosA+cosB)=1+2cosAcosB=16/25
cosAcosB=-9/50
cos(A-B)=cosAcosB+sinAsinB=-1/2
SIN(A+B)+COS(A+B)=或者＝根号2倍的cos(A+B-45度）＝根号2倍的[cos(A+B)cos45度+sin(A+B)sin45]
=1/2[cos(A+B)+sin(A+B)]
=2分之根号2倍的cos0
=2分之根号2 一、
(sinA+sinB)^2=(sinA)^2+2sinAsinB+(sinB)^2 (1)
(cosA+cosB)^2=(cosA)^2+2cosAcosB+(cosB)^2 (2)
cosAcosB+sinAsinB=cos(A-B) (3)
(sinA)^2+(cosA)^2=1 (4)
(sinB)^2+(cosB)^2=1 (5)
其中
sinA+sinB=3/5
cosA+cosB=4/5，
(1)(2)(3)(4)(5)各式两边各相加相消并代入数值得
1=2+2cos(A-B)
得cos(A-B)=-1/2

二、
(2)-