1 tan22°tan23°-tan22°-tan23°

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1 tan22°tan23°-tan22°-tan23°
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1 tan22°tan23°-tan22°-tan23°
1 tan22°tan23°-tan22°-tan23°

1 tan22°tan23°-tan22°-tan23°
=(sin22°sin23°)/(cos22°cos23°)-sin22°/cos22°-sin23°/cos23° (通分)
=(sin22°sin23°-(sin22°cos23°+sin23°cos22°))/(cos22°cos23°)
=(sin22°sin23°-sin45°)/(cos22°cos23°) (sin45°=cos45°)
=-1