Question 558690
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^3(x)\ =\ 3\sin(x)]


Divide both sides by *[tex \Large \sin(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^2(x)\ =\ 3]


Divide both sides by 4:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ =\ \frac{3}{4}]


Take the root of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ =\ \pm\frac{\sqrt{3}}{2}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\pi}{3}\ +\ k\pi\ \forall\ k\ \in\ \mathbb{Z}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{2\pi}{3}\ +\ k\pi\ \forall\ k\ \in\ \mathbb{Z}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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