对任意x,y属于R,恒有sinx+cosy=2sin(x-y\2+派\4)cos(x+y\2-派\4),则sin13派\24cos5派\24等于
问题描述：
对任意x,y属于R,恒有sinx+cosy=2sin(x-y\2+派\4)cos(x+y\2-派\4),则sin13派\24cos5派\24等于
答
x-y\2+派\4=13派\24
x+y\2-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-y\2+派\4)cos(x+y\2-派\4),所以
sin13派\24cos5派\24
= (sin3π/4+cosπ/6 )/2
= (√3+ √2 )/4