Solve the equation tanx+1/tanx=1+3tanx For 0<x<180?

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Answer 1 · 2017-11-13T19:26:21

$30^{o}$ $30^o$

$\frac{tan x + 1}{tan x} = 1 + 3 tan x$ $(tanx+1)/tanx=1+3tanx$

Multiply by $tan x$ $tanx$

$tan x + 1 = tan x + 3 {tan}^{2} x$ $tanx+1=tanx+3tan^2x$

$\to tan x + 1 - tan x - 3 {tan}^{2} x = 0$ $-> tanx+1-tanx-3tan^2x=0$

$->cancel(tanx)+1cancel(-tanx)-3tan^2x=0$

$->1-3tan^2x=0$

$->tan^2x=1/3=>tanx=+-sqrt(1/3)=-1/sqrt(3) and 1/sqrt(3)$

$x=tan^-1(tanx)=tan^-1(1/sqrt(3))=pi/6=30^o$