f(x)=2sin(x+a/2)cos(x+a/2)+2根号3cos^2(x+a/2)-根号3当a=π/3时,求满足f(x)>=1的x的集合
问题描述:
f(x)=2sin(x+a/2)cos(x+a/2)+2根号3cos^2(x+a/2)-根号3
当a=π/3时,求满足f(x)>=1的x的集合
答
化简的:f(x)=sin(2x+a)+cos(2x+a)
=根2*(cosπ/4*sin(2x+a)+sinπ/4cos(2x+a)
=根2*sin(2x+a+π/4)
因为a=π/3,
f(x)>=1
所以2kπ+π/4《2x+π/4+π/3《2kπ+3π/4
解的kπ-π/6《x《Kπ+π/6