f(x)=sin(x-π/4)+sin[π/2-(x+π/4)]
=sin(x-π/4)+sin(π/4-x)
=sin(x-π/4)-sin(x-π/4)
=0
所以是常函数
所以没有增区间你题目看错了吧，第二个是coscosx= sin(π/2-x)好吧，是我看错了