若f(a)=（2tana）-[（2sin^2a/2 -1）/sin(a/2)cos(a/2)]则f(兀/12)=

显示全部楼层 · 2009-2-14 21:38:31

千问 · 2009-2-14 21:38:31

由f(a)=（2tana）-[（2sin^2a/2 -1）/sin(a/2)cos(a/2)]先对f(a)进行化简f(a)=（2tana）-[-2(1-2sin^2a/2 )/2sin(a/2)cos(a/2)]
=(2tana)+2cosa/sina
=2(sina/cosa+cosa/sina)
=2[(sin^2a+cos^2a)/sinacosa]
=2/sinacosa
=4/sin2a所以f（π/12）=4/sin2π/12=8...