如何证明:当2kπ-π/4 0
问题描述：
如何证明:当2kπ-π/4 =sin x,sin x +cos x >0
答
和差化积：
sinx-cosx=√2[(√2/2)sinx-(√2/2)cosx]
=√2[sin(x-π/4)]
sinx+cosx=√2[(√2/2)sinx+(√2/2)cosx]
=√2[sin(x+π/4)]
所以
2kπ-π/4 2kπ-π/2√2[sin(x-π/4)]2kπ√2[sin(x+π/4)]>=0
所以sinx-cosx=0
得证