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# Find the solutions of the equation that are in the interval [0, 2𝜋).

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Find the solutions of the equation that are in the interval [0, 2𝜋).

tan^2 x sin x = 3 sin x

May 2, 2021

#1
+11414
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Find the solutions of the equation that are in the interval [0, 2𝜋).

Hello Guest!

$$tan^2 x sin x = 3 sin x\\ sinx(tan^2x-3)=0\\ sinx=0\\ \color{blue}x\in \{\ 0,\pi ,2\pi\}\\ tan^2x-3=0\\ tan^2x=3\\ tan\ x=\pm \sqrt{3}\\ x=atan(\pm \sqrt{3})$$

$$\color{blue}x\in \{\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\}$$

!

May 2, 2021
edited by asinus  May 2, 2021
edited by asinus  May 2, 2021
edited by asinus  May 2, 2021