tan(π/8)-1/(tan(π/8))的值为( -2 )

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tan(π/8)-1/(tan(π/8))的值为( -2 )
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tan(π/8)-1/(tan(π/8))的值为( -2 )
tan(π/8)-1/(tan(π/8))的值为( -2 )

tan(π/8)-1/(tan(π/8))的值为( -2 )
tan(π/4)=2tan(π/8)/(1-tan²(π/8))=1
∴1-tan²(π/8)=2tan(π/8)
原式=【tan²(π/8)-1】/tan(π/8)
=-2tan(π/8)/tan(π/8)
=-2

(tanπ/8)-1/(tanπ/8)
=(tan^2π/8-1)/(tanπ/8)
=2(tan^2π/8-1)/(2tanπ/8)
=-2/tanπ/4
=-2