计算tanπ/12 / (1-tan^2π/12)=
问题描述：
计算tanπ/12 / (1-tan^2π/12)=
答
tanx/(1-tan^2x)
=(sinx/cosx)/(1-sin^2x/cos^2x)
=(sinx/cosx)/((cos^2x-sin^2x)/cos^2x)
=sinxcosx/(1-sin^2x-sin^2x)
=2sinxcosx/2cos2x
=sin2x/2cos2x
=(1/2)tan2x
将x=π/12代入
原式=(1/2)tan2*π/12
=(1/2)tanπ/6
=√3/6
答
tanπ/12 / (1-tan^2π/12)
=1/2*(2tanπ/12) / (1-tan^2π/12)
=1/2*tan(π/12+π/12)
=1/2*tanπ/6
=1/2*√3/3
=√3/6