函数y=2+sinx-cosx的最大值

Question

过程是什么啊？

Answer 1

y=2+sinx-cosx
=2+√2(√2/2sinx-√2/2cosx)
=2+√2(sinxcosπ/4-cosxsinπ/4)
=2+√2sin(x-π/4)
所以最大值=2+√2

Answer 2

2+根号2