1、已知sina+cosb+4/5,cosa+sinb+3/5,求sin（a+b）,sin（a-b）

1、sina + cosb = 4/5 sin²a + 2sinacosb + cos²b = 16/25
cosa + sinb = 3/5 cos²a + 2cosasinb + sin²b = 9/25
两式相加 sin²a+cos²a+2(sinacosb+cosasinb)+cos²b+sin²b=1
1+2sin(a+b)+1 =1
sin(a+b) = - 1/2
两式相减 -cos(2a) + 2sin(a-b) +cos(2b) = 7/25
2sin(a-b) + 2sin(a+b)sin(a-b) = 7/25 【和差化积】
所以 sin(a-b) = 7/25
2、sina+sinb = 4/5 sin²a + 2sinasinb + sin²b = 16/25
cosa+cosb=3/5 cos²a+2cosacosb+cos²b = 9/25
两式相加 2cos(a-b) +2 = 1 cos(a-b) = - 1/2
两式相减 cos2a + 2cos(a+b) +cos2b = -7/25
2cos(a+b)cos(a-b) + 2cos(a+b) = -7/25
cos(a+b) = -7/25
tan(a+b) = (tana + tanb) / (1 - tanatanb)
= (sina + sinb) / (cosacosb - sinasinb)
= (sina+sinb) / cos(a+b)
= - 20/7
sin(a-b) = ±√[1- cos²(a-b)] = ±√3 /2

好好看看 是不是写错题目了