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?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 00:15:32
![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?](/uploads/image/z/1595895-15-5.jpg?t=%E5%8C%96%E7%AE%80%28tan5%CF%80%2F4%2Btan5%CF%80%2F12%29%2F%281-tan5%CF%80%2F12%29%28tan+5%CF%80%2F4+%2B+tan+5%CF%80%2F12%29%2F%281-tan+5%CF%80%2F12%29+%3D%28tan+%CF%80%2F4+%2B+tan+%CF%80%2F6%2B%CF%80%2F4+%29%2F%281-tan+%CF%80%2F4%2Atan+%CF%80%2F6%2B%CF%80%2F4+%29+%3Dtan%28%CF%80%2F4+%2B+%CF%80%2F6%2B%CF%80%2F4+%29%3Dtan%28%CF%80%2F2%2B%CF%80%2F6%29+%E8%AF%B7%E9%97%AE%E6%88%91%E8%BF%99%E6%A0%B7%E7%AE%97%E9%94%99%E5%9C%A8%E5%93%AA%E5%91%A2%3Ftan+%CF%80%2F2%E4%B8%8D%E6%98%AF%E6%97%A0%E6%84%8F%E4%B9%89%E5%90%97%3F)
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?
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?
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.
直接算结果就可以了,没必要拆分。tan(π/2+π/6)=tan(π-π/3)=tan(2/3π)=-根号3
做到这里没有错,你不要把它变成两个角用诱导公式
tan(π/2+π/6) = -cotπ/6) =-根号3