tanπ/12-1/tanπ/12=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/18 19:37:25
tanπ/12-1/tanπ/12=tanπ/12-1/tanπ/12=tanπ/12-1/tanπ/12==(sinπ/12)/(cosπ/12)-(cosπ/12)/(sinπ/12)=(sin&

tanπ/12-1/tanπ/12=
tanπ/12-1/tanπ/12=

tanπ/12-1/tanπ/12=
=(sinπ/12)/(cosπ/12)-(cosπ/12)/(sinπ/12)
=(sin²π/12-cos²π/12)/(sinπ/12*cosπ/12)
=2*(sin²π/12-cos²π/12)/(sinπ/6)
=2*(-cosπ/6)/(sinπ/6)
=-2/(tanπ/6)
=-2√3
(公式:tanA=sinA/cosA,sin2A=2sinAcosA,cos2A=2cos²A-1=1-2sin²A=cos²A-sin²A)

=sin15°/cos15°-cos5°/sin15°
=(sin²15°-cos²15°)/sin15°cos15°
=2(sin²15°-cos²15°)/sin30°
=-4cos30°=-2√3