Question

化简(tan5π/4+tan5π/12)/(1-tan5π/12)

Answer 1

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.