1、f(x)=-2asinx+2a+b (a>0)
∵a>0
∴h(x)=-2asinx在x∈[0,π/2]是单调递减函数
f(x)=-2asinx+2a+b在x∈[0,π/2]是单调递减函数
f(0)=2
-2asin0+2a+b=2
2a+b=2.(1)
f(π/2)=0
-2asinπ/2+2a+b=0
-2a+2a+b=0.(2)
b=0
代入(1)
2a+0=2
a=1
2、f(x)=-2sinx+1+0
f(x)=1-2sinx
g(x)=f(x+π/2)
=1-2sin(x+π/2)
=1-2cosx
g(x)在[2kπ,π+2kπ]是单调递减函数；
g(x)在[-π+2kπ,2kπ]是单调递增函数