化简(tan5π/4+tan5π/12)/(1-tan5π/12)

问题描述:

化简(tan5π/4+tan5π/12)/(1-tan5π/12)
(tan 5π/4 + tan 5π/12)/(1-tan 5π/12)
=(tan π/4 + tan π/6+π/4 )/(1-tan π/4*tan π/6+π/4 )
=tan(π/4 + π/6+π/4 )
=tan(π/2+π/6)
请问我这样算错在哪呢?tan π/2不是无意义吗?

......
=tan(π/2+π/6) 你做得到这里,都是对的.
tan(π/2+π/6)≠tan(π/2),而且tan(π/2+π/6)不能用两角和的三角函数公式展开,而要用“任意角的三角函数的诱导公式求解,即:
tan(π/2+π/6)=-cotπ/6=-√3.