3. tan(3x – $\frac{2\pi}{3}$ ) + cot x = 0 ; x ∈ ( $-\pi$ ; $\pi$ )

3. tan(3x – $\frac{2\pi}{3}$ ) + cot x = 0 ; x ∈ ( $-\pi$ ; $\pi$ )

0 thoughts on “3. tan(3x – $\frac{2\pi}{3}$ ) + cot x = 0 ; x ∈ ( $-\pi$ ; $\pi$ )”

  1. ĐK: $\cos(3x – \dfrac{2\pi}{3} ) \neq 0$ và $\sin x \neq 0$
    Tương đương vs $x  \neq \dfrac{7\pi}{18} + \dfrac{k\pi}{3}$ và $x \neq k\pi$

    Ptrinh đã cho tương đương vs

    $\tan (3x – \dfrac{2\pi}{3}) = -cot x = cot(-x)$

    $\Leftrightarrow \tan (3x – \dfrac{2\pi}{3}) = tan (x + \dfrac{\pi}{2} )

    $\Leftrightarrow 3x – \dfrac{2\pi}{3} = x + \dfrac{\pi}{2} + k\pi$

    $\Leftrightarrow x = \dfrac{7\pi}{12} + \dfrac{k\pi}{2}$

    Vậy $x = \dfrac{7\pi}{12} + \dfrac{k\pi}{2}$.

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