GPT :        $\sin(\pi \cos x )=1$.
ừh nhĩ. thế rồi cosx =1/2 cộng k rùi sao nữa ta :)) –  Đậu Đại Học 20-02-13 06:17 PM
Bài này nhìn lạ nhưng cách làm vẫn rất cơ bản
      $\sin (\pi \cos x)=1=\sin \dfrac{\pi}{2}$
$\Leftrightarrow \pi \cos x= \dfrac{\pi}{2}+k2\pi, \quad k \in \mathbb Z.$
$\Leftrightarrow \cos x= \dfrac{1}{2}+2k, \quad k \in \mathbb Z.$
Chú ý rằng $-1 \le \cos x \le 1, \quad \forall x$ nên ta phải có
$\begin{cases}k \in \mathbb Z \\ -1 \le  \dfrac{1}{2}+2k \le 1 \end{cases}\Leftrightarrow \begin{cases}k \in \mathbb Z \\ -\dfrac{3}{4} \le k \le \dfrac{1}{4} \end{cases}\Leftrightarrow k=0.$
Ta phải có
$ \cos x= \dfrac{1}{2}\Leftrightarrow x=\pm \dfrac{\pi}{3}+m2\pi, \quad m \in \mathbb Z.$
Hãy ấn chữ V dưới chữ đáp án để chấp nhận nếu như bạn thấy lời giải này chính xác, và nút mũi tên màu xanh để vote up nhé. Thanks! –  Trần Nhật Tân 20-02-13 07:13 PM

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