若f(x)=2tanx+【2sin²(x/2) -1除以sin(x/2)cos(x/2)】,则f(π/12)的值为?

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若f(x)=2tanx+【2sin²(x/2)-1除以sin(x/2)cos(x/2)】,则f(π/12)的值为?若f(x)=2tanx+【2sin²(x/2)-1除以sin(x/

若f(x)=2tanx+【2sin²(x/2) -1除以sin(x/2)cos(x/2)】,则f(π/12)的值为?
若f(x)=2tanx+【2sin²(x/2) -1除以sin(x/2)cos(x/2)】,则f(π/12)的值为?

若f(x)=2tanx+【2sin²(x/2) -1除以sin(x/2)cos(x/2)】,则f(π/12)的值为?
f(x)=2tanx+【2sin²(x/2) -1除以sin(x/2)cos(x/2)】
=2tanx-cosx/(1/2sinx)
=2sinx/cosx-2cosx/sinx
=2(sin^2x-cos^2x)/sinxcosx
=-4cos2x/sin2x
f(π/12)=-4(cosπ/6)/(sinπ/6)
=-4(√3/2)/(1/2)
=-4√3