Question

把函数y=√3sinx+cosx-m的图像向左平移π/6个单位，再把横坐标缩小到原来的2倍，得到

数g(x),当x∈[0,π/2]是，函数g(x)的两零点为x1,x2则tan[-(x1+x2)]为？

Answer 1

解y=√3sinx+cosx-m
=2(√3/2sinx+1/2cosx)-m
=2sin(x+π/6)-m
又由向左平移π/6个单位，再把横坐标缩小到原来的2倍，得到
函数g(x)=2sin(2x+π/3)-m
又由x属于[0,π/2]

则2x属于[0,π]
则2x+π/3属于[π/3,4π/3],
又由当x∈[0,π/2]是，函数g(x)的两零点为x1,x2，

则知2x1+π/3+2x2+π/3=2×π/2
即2x1+2x2=π/3
则x1+x2=π/6
则tan[-(x1+x2)]

=tan(-π/6)
=-√3/3