tan(x+π/4)+tan(x-π/4)化简得

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 06:36:40
tan(x+π/4)+tan(x-π/4)化简得tan(x+π/4)+tan(x-π/4)化简得tan(x+π/4)+tan(x-π/4)化简得tan(x+π/4)+tan(x-π/4)设a=x+π/

tan(x+π/4)+tan(x-π/4)化简得
tan(x+π/4)+tan(x-π/4)化简得

tan(x+π/4)+tan(x-π/4)化简得
tan(x+π/4)+tan(x-π/4)
设a=x+π/4,则x-π/4=a-π/2
原式=tana+tan(a-π/2)
=tana-cota
=sina/cosa-cosa/sina
=-2cos2a/sin2a
=-2cot2a
=-2cot(2x+π/2)
=2cot(-2x-π/2)
=2cot(π/2-2x)
=2tan2x