F(X)=A＜2COS^2（X／2）＋SinX＞＋B,A小于0,且X属于0到180度,函数F的值域为3到4,求A＋B的值

F(X)=A(CosX+1+SinX)+B
=A(CosX+SinX)+A+B
=2^1/2*A*Sin(x+pi/4)+A+B
当x属于[0,pi]时,Sin(x+pi/4)属于[-2^(-1/2),1]
又A小于0,因此当Sin(x+pi/4)=-2^(-1/2)时,F(x)=4
Sin(x+pi/4)=1时,F(x)=3,即
2^1/2*A*[-2^(-1/2)]+A+B=4
2^1/2*A*1+A+B=3
解方程组得A=1-2^(1/2)B=4
A+B=5-2^(1/2)