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tan2x=3tanx
=>(2tanx/(1-((tanx)^2))=3tanx
=>2tanx=3tanx(1-((tanx)^2))
=>2tanx=3tanx-3((tanx)^3)
=>3((tanx)^3)-tanx=0
=>tanx(3((tanx)^2)-1)=0
=>tanx=0 OR tanx=(1/sqrt(3)) OR tanx=-(1/sqrt(3))
tanx=0=>x=arctan(0)=0, (Pi), 2(Pi)
tanx=(1/sqrt(3))=>x=arctan(1/sqrt(3))=((Pi)/6), (7/6)(Pi)
tanx=arctan(-(1/sqrt(3)))=-arctan((1/sqrt(3)))
Supposing that the range, 0<=R<=(2(Pi)), tanx=-(1/sqrt(3))) does not give a valid range of values, so:
x=0, ((Pi)/6), (Pi), (7/6)(Pi), 2(Pi)
Newton.
=>(2tanx/(1-((tanx)^2))=3tanx
=>2tanx=3tanx(1-((tanx)^2))
=>2tanx=3tanx-3((tanx)^3)
=>3((tanx)^3)-tanx=0
=>tanx(3((tanx)^2)-1)=0
=>tanx=0 OR tanx=(1/sqrt(3)) OR tanx=-(1/sqrt(3))
tanx=0=>x=arctan(0)=0, (Pi), 2(Pi)
tanx=(1/sqrt(3))=>x=arctan(1/sqrt(3))=((Pi)/6), (7/6)(Pi)
tanx=arctan(-(1/sqrt(3)))=-arctan((1/sqrt(3)))
Supposing that the range, 0<=R<=(2(Pi)), tanx=-(1/sqrt(3))) does not give a valid range of values, so:
x=0, ((Pi)/6), (Pi), (7/6)(Pi), 2(Pi)
Newton.
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