1.已知2sin（3派+b）=cos（派+b），求2sin^2b+3sinbcosb-cos^2b的值。
2.已知函数f（x）=2sin9x+派/3）-2sinx，x属于[-派/2，0]。（1）若cosx=根号3/3，求函数f（x）的值。（2）求函数f（x）的值域。

1.已知2sin(3π + β) = cos(π + β)，求2(sinb)^2 + 3sinβcosβ - (cosβ)^2的值。

sin(3π + β)
= sin(2π + π + β)
= sin(π + β)
= -sinβ

cos(π + β) = -cosβ

-2sinβ = -cosβ
cosβ = 2sinβ
cotβ = 2

2(sinβ)^2 + 3sinβcosβ - (cosβ)^2
= 2(sinβ)^2+ 6(sinβ)^2 - 4(sinβ)^2
= 4(sinβ)^2
= 4{1/[1 + (cotβ)^2]}
= 4/5

2、已知函数f(x) = 2sin(x + π/3) - 2sinx，x属于[-π/2，0]。

(1)若cosx = √3/3，求函数f(x)的值。
sinx = -√[1 - (cosx)^2]
= -√[1 - (√3/3)^2]
= -√6/3

f(x) = 2(sinxcosπ/3 + cosxsinπ/3) - 2sinx
= 2[-√6/3×1/2 + √3/3×(√3/2)] - 2×(-√6/3)
= √6/3 + 1


(2)求函数f(x)的值域。
f(x) = 2sin(x + π/3) - 2sinx
= 2×2×cos(x + x - π/3)×sin(x + π/3 - x)
= 2√3cos(2x - π/3)

最小值:f(-π/2) = -√3
最大值:f(0) = √3

即 -√3≤f(x)≤√3