f(x)=2cos(x/2)sin(x/2-π/6) 若x∈(0,π/2) f(x)=-1/6 求cosx的值
问题描述：
f(x)=2cos(x/2)sin(x/2-π/6) 若x∈(0,π/2) f(x)=-1/6 求cosx的值
答
f(x)=sin(x/2-π/6+x/2)-sin(x/2-π/6-x/2)
=sin(x-π/6)+sin(π/6)
=sin(x-π/6)+1/2
f(x)=-1/6
sin(x-π/6)=1/3cos(x-π/6)=2√2/3
cosx=cos(x-π/6)cos(π/6)-sin(x-π/6)sin(π/6)
=(2√6-1)/6f(x)=sin(x/2-π/6+x/2)-sin(x/2-π/6-x/2) 应该是f(x)=sin(x/2-π/6+x/2)+sin(x/2-π/6-x/2)吧？谢谢提醒，修正如下：f(x)=sin(x/2-π/6+x/2)+sin(x/2-π/6-x/2) =sin(x-π/6)-sin(π/6)=sin(x-π/6)-1/2