cos3x+cos5x=0

题目

cos3x+cos5x=0
过程.谢谢.

答案

cos3x+cos5x=0
cos(4x-x)+cos(4x+x)=0
cos4xcosx+sin4xsinx+cos4xcosx-sin4xsinx=0
cos4xcosx=0
(i)若cosx=0
则x=kπ+π/2(k∈Z)
(ii)若cos4x=0
则x=kπ/4+π/8(k∈Z)
所以解集是{x|x=kπ+π/2或x=kπ/4+π/8(k∈Z)}