已知tan(a+π/4)=-1/2,π/2

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/22 01:55:28
已知tan(a+π/4)=-1/2,π/2已知tan(a+π/4)=-1/2,π/2已知tan(a+π/4)=-1/2,π/2(1)tan(A+π/4)=-1/2[tanA+tan(π/4)]/(1-

已知tan(a+π/4)=-1/2,π/2
已知tan(a+π/4)=-1/2,π/2

已知tan(a+π/4)=-1/2,π/2
(1)
tan(A+π/4)=-1/2
[tanA+tan(π/4)]/(1-tanA.tanπ/4)=-1/2
(tanA+1)/(1-tanA)=-1/2
2tanA+2 = -1+tanA
tanA = -3
A=arctan(-3) =108.43°
(2)
tanA = -3
=> sinA = 3/√10 and cosA=-1/√10
[sin2A - 2(cosA)^2]/√2sin(A-π/4)
=[2sinA.cosA - 2(cosA)^2]/√2[sinA.cos(π/4)-cosA.sin(π/4)]
=[2(-3/10) - 2(1/10)]/[3/√10 +1/√10]
=-(8/10).(√10/4)
=-2√10/10