πcosx=-πsinx+π/2
cosx+sinx=1/2
sin(x+π/4)=1/2√2
x+π/4=arcsin(1/2√2)+2kπ 或 x+π/4=π-arcsin(1/2√2)+2kπ
x=-π/4+arcsin(1/2√2)+2kπ x=3π/4-arcsin(1/2√2)+2kπ非常感谢您的回答！我刚学，书上的答案：x=2kπ±arccos(1/2√2)±π/4,能看一下和你答案的联系和区别吗？弄懂此题，加你30分，略表谢意！再一次谢谢！谢谢，用arccos(1/2√2)形式更简洁cosx+sinx=1/2√2cos(x-π/4)=1/2cos(x-π/4)=1/2√2cos a= cos(-a)x-π/4=arccos(1/2√2)+2kπ或π/4-x=arccos(1/2√2)-2kπx=2kπ+arcos(1/2√2)+π/4 x=2kπ-(arccos1/2√2)+π/4x=2kπ±arccos(1/2√2)+π/4