help me please: tan3x-tanx-1=0 ​

Question

help me please: tan3x-tanx-1=0

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Huyền Thanh 1 year 2021-09-01T09:10:27+00:00 1 Answers 3 views 0

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    2021-09-01T09:11:45+00:00

    Answer: [tex]x=0.30714\dots +\pi n[/tex]

    Step-by-step explanation:

    [tex]\Rightarrow \tan3x-\tan x-1=0\\\\\Rightarrow \dfrac{3\tan x-\tan ^3x}{1-3\tan ^2x}-\tan x-1=0\\\\\Rightarrow 3\tan x-\tan ^3x+( 1-3\tan ^2x)(-1-\tan x)=0\\\Rightarrow 3\tan x-\tan ^3x-1-\tan x+3\tan ^2x+3\tan ^3 x=0\\\Rightarrow 2\tan ^3x+3\tan ^2x+2\tan x-1=0\\\Rightarrow \tan \left(x\right)\approx \:0.31718[/tex]

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