sin2A=1,tan(A+60)为多少?

sin2A=1,tan(A+60)为多少?
sin2A=1,tan(A+60)为多少?

sin2A=1,tan(A+60)为多少?
sin(2A)=1,
2A=90°,
A=45°
tan(A+60°)
=tan(45°+60°)
=(tan45°+tan60°)/(1-tan45°tan60°)
=(1+√3)/(1-1*√3)
=-2-√3
如仍有疑惑,欢迎追问.

sin2A=1==>2A=π/2+2Kπ
A=π/4+Kπ
A+π/3=7/12π+Kπ
tan(A+π/3)=tan(7/12π+Kπ)=tan7/12π=tan(π/4+π/3)
=[1+√3]/[1-√3]=-2-√3

sin2A = 1
A = 180°k + 45°
tan (A + 60°) = tan(180°k + 105°) = tan105° = - cot15° = - (√3 + 2)