tan1^0tan2^0 tan3^0 tan44^0 tan45^0 tan46^0tan88^0tan89^0

先证一个公式.tanα·tna(90°-α)=1
tanα·tna(90°-α)=sinα·sin(90°-α)／[cosα·cos(90°-α)]=sinα·cosα/cosα·sinα=1
所以　tan1°·tan89°=1,tan2°·tan88°=1,...,tan44°·tan46°=1
从而　tan1°·tan2°·tan3°·...·tan89°=tan45°=1