化简(tan5π/4+tan5π/12)/(1-tan5π/12)
问题描述：
化简(tan5π/4+tan5π/12)/(1-tan5π/12)
答
根据tan的和角公式：
tan(x+y)=(tanx+tany)/(1-tanxtany)
再根据诱导公式：tan 5π/4 = tan(π+π/4) =tan π/4
所以
(tan 5π/4 + tan 5π/12)/(1-tan 5π/12) (诱导公式,并利用tan π/4=1)
=(tan π/4 + tan 5π/12)/(1-tan π/4*tan 5π/12) (由tan的和角公式)
=tan(π/4 + 5π/12)
=tan 2π/3
=-根号3
综上,原式= -根号3.