Giải pt:2sin4x-1=0 Tìm txđ: y=cot+1:1+tan ²x Tìm txđ:y=cos √x+1:x
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1) $2\sin 4x-1=0$ $\Rightarrow \sin 4x=\dfrac{1}{2}$ $\Rightarrow \left[ \begin{array}{l} 4x=\dfrac{\pi}{6}+k2\pi \\ 4x=\pi-\dfrac{\pi}{6}+k2\pi\end{array} \right .$ $\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{24}+k\dfrac{\pi}{2} \\x=\dfrac{5\pi}{24}+k\dfrac{\pi}{2}\end{array} \right .(k\in\mathbb Z)$ 2) $y=\dfrac{\cot x+1}{1+{\tan}^2x}$ Đk: $\left\{ \begin{array}{l} \sin x\ne0 \\ \cos x\ne0 \end{array} \right .$ $\Leftrightarrow\sin 2x\ne0$ $\Leftrightarrow 2x\ne k\pi$ $\Leftrightarrow x\ne k\dfrac{\pi}{2}(k\in\mathbb Z)$ 3) $y=\cos\sqrt{x}+\dfrac{1}{x}$ Đk: $\left\{ \begin{array}{l} x\ge0\\ x\ne0 \end{array} \right .$ $\Leftrightarrow x>0$
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