题目

对任意x,y属于R,恒有sinx+cosy=2sin(x-y2+派4)cos(x+y2-派4),则sin13派24cos5派24等于

提问时间：2021-03-30

答案

x-y2+派4=13派24
x+y2-派4=5派24
解得x=3π/4,y= π/6
对任意x,y属于R,恒有sinx+cosy=2sin(x-y2+派4)cos(x+y2-派4),所以
sin13派24cos5派24
= (sin3π/4+cosπ/6 )/2
= (√3+ √2 )/4