化简:tan(π/8)+1/tan(π/12)

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化简:tan(π/8)+1/tan(π/12)

化简:tan(π/8)+1/tan(π/12)
化简:tan(π/8)+1/tan(π/12)

化简:tan(π/8)+1/tan(π/12)
tanα=sinα/cosα
=2s²inα/(2sinαcosα﹚
=[1-cos(2α﹚]/sin﹙2α﹚
∴tan(π/8)=√2-1
1/tan(π/12)=2+√3
∴tan(π/8)+1/tan(π/12)=√2+√3+1