化简f(x)=2cos(x/2)·(sin(x/2)+cos(x/2))-1
问题描述：
化简f(x)=2cos(x/2)·(sin(x/2)+cos(x/2))-1
(1)化简f(x);
(2)求f(π/12)的值
答
（1）f(x)=2cos(x/2)·(sin(x/2)+cos(x/2))-1
=2cos(x/2)·sin(x/2)+2cos^2(x/2)-1
=sinx+cosx (倍角公式)
=√2sin(x+π/4)
（2）f(π/12)=√2sinπ/3=√6/2