# Equating trigonometric identities: <msqrt> 3 </msqrt> cos &#x2061;<!-- ⁡ --> (

Equating trigonometric identities: $\sqrt{3}\mathrm{cos}\left(x\right)-\mathrm{sin}\left(x\right)=0,x\in \left[-\pi ,\pi \right]$
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behk0
$\sqrt{3}\mathrm{cos}\left(x\right)=\mathrm{sin}\left(x\right)$
$\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\sqrt{3}=\frac{\mathrm{sin}x}{\mathrm{cos}x}=?$
$\mathrm{tan}x=\mathrm{tan}\frac{\pi }{3}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}x=n\pi +\frac{\pi }{3}$
where n is any integer.
Choose n such that $x\in \left[-\pi ,\pi \right]$

ntaraxq
$\sqrt{3}\mathrm{cos}x-\mathrm{sin}x=0$
Dividing both sides by 2.
$\frac{\sqrt{3}}{2}\mathrm{cos}x-\frac{1}{2}\mathrm{sin}x=0
$\mathrm{sin}{60}^{\circ }\cdot \mathrm{cos}x-\mathrm{cos}{60}^{\circ }\cdot \mathrm{sin}x=0
$\mathrm{sin}\left(60-x{\right)}^{\circ }=0
$x={60}^{\circ },{120}^{\circ }$