蓝冰之剑
幼苗
共回答了18个问题采纳率:83.3% 举报
f(x) = cos(x+b)+sin(x+b)
= 根号2 * sin(x+b+π/4)
若f(x)是奇函数,则f(-x) = -f(x)
即
(根号2) * sin(b+π/4-x) = -(根号2) * sin(b+π/4+x)
也即sin(x-b-π/4) = sin(x+b+π/4)
所以有x - b-π/4 = 2kπ + x + b + π/4
或者x - b-π/4 + x + b + π/4 = kπ
即2b + π/2 +2kπ =0或者2x = kπ,后者不具有一般性,故舍去.
2b + π/2 +2kπ =0可转化为
b = kπ - π/4
在A,B,C,D中,只有D符合,
所以选D
1年前
5