# Solve the equations and show all the solutions in the first quadrant 3\ta

Solve the equations and show all the solutions in the first quadrant
$3\mathrm{tan}\theta -\mathrm{cot}\theta =0$
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Nichole Watt
Use the trigonometry ratio
$3\mathrm{tan}\theta -\mathrm{cot}\theta =0$
$⇒3\mathrm{tan}\theta =\mathrm{cot}\theta$
$⇒\frac{3\mathrm{tan}\theta }{\mathrm{cot}\theta }=1$
$⇒\mathrm{tan}±\theta =\frac{1}{\sqrt{3}}$
$⇒\theta ={\mathrm{tan}}^{-1}\left(±\frac{1}{\sqrt{3}}\right)$
$=±{\mathrm{tan}}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$=±\frac{\pi }{6}$
Solutioms in the first quadrant is $\theta =\frac{\pi }{6}$
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Jeffrey Jordon

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