tanAtanB+tanBtanC+tanCtanA=tanAtanB+(tanA+tanB)ctan(B+A) (by A+B+C=90°)
=(sinAsinB)/(cosAcosB)+[(sinA/cosA)+(sinB/cosB)]cos(A+B)/sin(A+B)
=(sinAsinB)/(cosAcosB)+[(sinAcosB+sinB+cosA)/(cosAcosB)]cos(A+B)/sin(A+B)
=(sinAsinB)/(cosAcosB)+cos(A+B)/(cosAcosB)
=1
A+B+C=90°,证明tanAtanB+tanBtanC+tanCtanA=1(详细过程)
A+B+C=90°,证明tanAtanB+tanBtanC+tanCtanA=1(详细过程)
数学人气:141 ℃时间:2020-05-07 13:48:23
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