y=-1/2（t-1）平方+1.t=sinx-cosx=根号2sin(x-π/4)请问这步怎么换算得到的?

题目

y=-1/2（t-1）平方+1.t=sinx-cosx=根号2sin(x-π/4)请问这步怎么换算得到的?

答案

t=sinx-cosx
t=√2[(√2 / 2)sinx - (√2 / 2)cosx]
t=√2(sinx * cosπ/4 - cosx * sinπ/4)
t=√2sin(x - π/4)