How do you solve $3 {tan}^{2} x = 1$ $3tan^2x = 1$ ?

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Answer 1 · 2015-11-14T06:48:16

$x$ $x$ = $30^{o}$ $30^o$ , $150^{o}$ $150^o$ , $210^{0}$ $210^0$ , $330^{0}$ $330^0$

The given quadratic equation = $3 {tan}^{2}$ $3tan^2$ = $1$ $1$

${tan}^{2} x$ $tan^2x$ = $\frac{1}{3}$ $1/3$

Finding square root on both sides

$tan x$ $tanx$ = $\pm$ $+-$ $\frac{1}{\sqrt{3}}$ $1/sqrt3$

Taking +ve value

$tan x$ $tanx$ = $\frac{1}{\sqrt{3}}$ $1/sqrt3$

$tan x$ $tanx$ = ${tan 30}^{0}$ $tan30^0$

$x$ $x$ = $30^{0}$ $30^0$

since x is positive, x is positive in first or third quadrant

So, $x$ $x$ = $30^{0}$ $30^0$ or $180^{0}$ $180^0$ + $30^{0}$ $30^0$
= $30^{0}$ $30^0$ or $210^{0}$ $210^0$

Again taking -ve value

$tan x$ $tanx$ = $- \frac{1}{\sqrt{3}}$ $-1/sqrt3$

Since tan will have negative value in second and fourth quadrant

$x$ $x$ = $180 - 30$ $180-30$ or $360 - 30$ $360-30$

$x$ $x$ = $150^{o}$ $150^o$ or $330^{o}$ $330^o$

Hence $x$ $x$ = $30^{o}$ $30^o$ , $150^{o}$ $150^o$ , $210^{0}$ $210^0$ , $330^{0}$ $330^0$

How do you solve 3tan^2x = 13tan2x=13tan^2x = 1?