化简:tan4分之5派+tan12分之5派/1-tan12分之5派应从何入手 /.

分类: 作业答案 • 2021-12-19 15:48:46

问题描述：

化简:tan4分之5派+tan12分之5派/1-tan12分之5派
应从何入手 /.

答

根据周期性：tan(5π/4) = tan[(5π/4) - π] = tan(π/4) = 1
∴原式 = {tan(π/4) + tan(5π/12)}/{1 - [tan(π/4)]·[tan(5π/12)]}
= tan[(π/4) + (5π/12)]
= tan(2π/3)
= -√3