作业帮化简(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?
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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?
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=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