4(tan角A)=tan(3角A) 求角A

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/25 00:08:47
4(tan角A)=tan(3角A)求角A4(tan角A)=tan(3角A)求角A4(tan角A)=tan(3角A)求角A4tanA=tan(3A),∴4sinA/cosA=sin(3A)/cos(3A

4(tan角A)=tan(3角A) 求角A
4(tan角A)=tan(3角A) 求角A

4(tan角A)=tan(3角A) 求角A
4tanA = tan(3A),∴4sinA/cosA = sin(3A)/cos(3A)
∴4sinA·cos(3A) = sin(3A)·cosA
积化和差可得:
原式左边 = 2(sin4A - sin2A)
原式右边 = (1/2)·(sin4A + sin2A)
∴4sin4A - 4sin2A = sin4A + sin2A
∴3sin4A = 5sin2A ,∴6cos2A = 5 ,
∴cos2A = 5/6 = [1 - (tanA)^2]/[1 + (tanA)^2]
令x = tanA ,则:5 + 5x^2 = 6 - 6x^2
∴x = ±√(1/11) = tanA
∴A = ±arctan√(1/11)