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Find all the solutions of the equation csc x tan x=2√3/3 on the interval [0,2π).

 Jun 28, 2020
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\(\csc x \tan x = \dfrac1{\sin x} \cdot \dfrac{\sin x}{\cos x} = \dfrac1{\cos x} \)

 

\(\dfrac1{\cos x} = \dfrac{2\sqrt 3}3\\ \dfrac1{\cos x} = \dfrac{2}{\sqrt 3}\\ \cos x = \dfrac{\sqrt 3}{2}\\ x = \dfrac{\pi}{6} \text{ or } x = \dfrac{11\pi}{6}\)

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 Jun 29, 2020

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