若f(x)=2tan x-(2sin²(x/2)-1)/(sin(x/2)cos(x/2)),则f(π/12)的值为多少?
f(x)=2tan x-(2sin²(x/2)-1)/(sin(x/2)cos(x/2))
=2tan x-(-cos x)/((sin x)/2)
=2sin x/cos x+2cos x/sinx
=2(sin²x+cos²x)/(sinxcosx)
=2/(sin(2x)/2)
=4/sin(2x)
f(π/12)=4/sin(π/6)=4/(1/2)=8
答：f(π/12)的值为8.