已知 tanx=2,则tan(2(x-π/4))等于

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已知 tanx=2,则tan(2(x-π/4))等于
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已知 tanx=2,则tan(2(x-π/4))等于
已知 tanx=2,则tan(2(x-π/4))等于

已知 tanx=2,则tan(2(x-π/4))等于
如图所示,可以再追问


tan[2(x-π/4)]=2[tan(x-π/4)]/{1-[tan(x-π/4)]^2}
={2[tanx-tan(π/4)]/[1+tanxtan(π/4)]}/{1-{[tanx-tan(π/4)]/[1+tanxtan(π/4)]}^2}
=[2(2-1)/(1+2×1)]/{1-[(2-1)/(1+2×1)]^2}
=(2/3)/[1-(1/3)^2]
=(2/3)/(8/9)
=(2/3)×(9/8)
=3/4