cos2x/sin{x-π/4}=-根号2/2求cosx+sinx的值

问题描述:

cos2x/sin{x-π/4}=-根号2/2求cosx+sinx的值

cos2x/sin{x-π/4}=(cos²x-sin²x)/[ 根号2/2(sinx-cosx)]
=-根号2 (cosx+sinx)
由已知得,-根号2 (cosx+sinx) =-根号2/2,
所以cosx+sinx=1/2.