已知函数f(x)=Sin(x-派/6)+cos(x-派/3),g(x)=2sin^2（x/2）.

题目

已知函数f(x)=Sin(x-派/6)+cos(x-派/3),g(x)=2sin^2（x/2）.
(I)若a是第一象限角,且f(a)=3倍根号3/5.求g(a)的值.(II)求使f(x)大于等于g(x)成立的X的取值集合.

答案

（1）f(x)=sin(x-π/6)+cos(x-π/3)
=sinxcosπ/6-cosxsinπ/6+cosxcosπ/3+sinxsinπ/3
=√3/2sinx-1/2cosx+1/2cosx+√3/2sinx
=√3sinx
g(x)=2sin^2(x/2)
=1-cosx
a是第一象限的角
f(a)=3√3/5
√3sina=3√3/5
sina=3/5
cosa=√(1-sin^2a)
=√(1-(3/5)^2)
=4/5
g(a)=1-cosa
=1-4/5
=1/5
（2）f(x)>=g(x)
√3sinx>=1-cosx
√3sinx+cosx>=1
2(√3/2sinx+1/2cosx)>=1
sin(x+π/6)>=1/2
π/6+2kπ=