函数y=sin(x+π/3)-sinx(x∈(0,π/2))的值域为
问题描述:
函数y=sin(x+π/3)-sinx(x∈(0,π/2))的值域为
a.-2,2 b,-1/2,√3/2 c.1/2,1 d.1/2,√3/2
答
sin(X+π/3)-sinx
=√3/2cosx-1/2sinx
=cos(x+π/6)
x∈(0,π/2)
则x+π/6∈(π/6,2π/3)
所以原式值域为(-1/2,√3/2 ),选B