(tan105°-1)/(tan105°+1)的值为

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(tan105°-1)/(tan105°+1)的值为
(tan105°-1)/(tan105°+1)的值为

(tan105°-1)/(tan105°+1)的值为
(tan105°-1)/(tan105°+1)
=[tan(180-75)-tan45]/[1+tan45*tan(180-75)]
=-(tan75+tan45)/(1-tan45*tan75)
=-tan(75+45)
=-tan120
=√3

(tan105+1)/(1-tan105)
=(tan105+tan45)/(1-tan45*tan105)
=tan(105+45)
=tan150
=-√3/3
所以(tan150-1)/(tan105+1)
=-1/[(tan105+1)/(1-tan105)]
=-1/(-√3/3)
=√3