[tex] \cos(x) ( \tan(x) - \sqrt{3} ) = 0[/tex]
[tex] \cos(x) ( \frac{ \sin(x) }{ \cos(x) } - \sqrt{3} ) = \\ [/tex]
Thus :
[tex] \cos(x) = 0 \: \: \: or \: \: \: \tan(x) - \sqrt{3} = 0[/tex]
Over interval [0 , 2pie ) :
[tex] \cos(x) = 0[/tex]
[tex]x = \frac{\pi}{2} , \frac{3\pi}{2} \\ [/tex]
And
[tex] \tan(x) - \sqrt{3} = 0[/tex]
[tex] \tan(x) = \sqrt{3} [/tex]
[tex]x = \frac{\pi}{3} ,\pi + \frac{\pi}{3} \\ [/tex]
[tex]x = \frac{\pi}{3} , \frac{4\pi}{3} \\ [/tex]
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Thus the solutions are :
[tex] \frac{\pi}{3} , \frac{\pi}{2} , \frac{4\pi}{3} , \frac{3\pi}{2} \\ [/tex]
As u can see the first option is the correct answer .
And we're done....
Have a great day ♡♡♡♡♡
