怎么样证明|sin(x-y)|≤|sin(x-z)|+|sin(z-y)|
问题描述：
怎么样证明|sin(x-y)|≤|sin(x-z)|+|sin(z-y)|
答
∵|cosx|≤1
|sin(x-y)|=|sin(x-y-z+z)|=|sin[(x-z)-(y-z)]|
=|sin[(x-z)cos(y-z)-cos(x-z)sin(y-z)|
=|sin[(x-z)cos(y-z)+cos(x-z)sin(z-y)|
≤|sin[(x-z)cos(y-z)|+|cos(x-z)sin(z-y)|
≤|sin[(x-z)|+|sin(z-y)|