tan70+tan50- √3tan70tan50＝?

来源：学生作业帮助网编辑：作业帮时间：2024/05/06 17:29:57

tan70+tan50- √3tan70tan50＝?
tan70+tan50- √3tan70tan50＝?

tan70+tan50- √3tan70tan50＝?
tan70+tan50- √3tan70tan50＝?
tan120=tan(70+50)=(tan70+tan50)/(1-tan50*tan70)
tan70+tan50=-√3*(1-tan50*tan70)
带入:原式=-√3+√3tan50*tan70- √3tan70tan50
=-√3

tan120=(tan70+tan50)/(1-tan70*tan50)=-sqrt(3).
so
tan70+tan50-sqrt(3)*tan70*tan50=-sqrt(3)

tan120=(tan70+tan50)/(1-tan70tan50)=-√3
tan70+tan50=√3tan70tan50-√3
tan70+tan50-√3tan70tan50=-√3

根据tan（A+B)=(tanA+tanB)/(1-tanAtanB)
∴tan(70+50)
=(tan70+tan50)/(1-tan70tan50)
=tan120
=-√3
∴ tan70+tan50- √3tan70tan50
=-√3(1-tan70tan50)-√3tan70tan50
=-√3+√3tan70tan50 -√3tan70tan50
=-√3

tan(70+50)
=(tan70+tan50)/(1-tan70tan50)
=tan120
=-√3
所以：
tan70+tan50=-√3(1-tan70tan50)
=-√3+√3tan70tan50
所以：tan70+tan50- √3tan70tan50=-√3

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