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1.
\(\left\{{}\begin{matrix}cos2x\ne0\\\sqrt{3}sin2x-cos2x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2x\ne\frac{\pi}{2}+k\pi\\\frac{\sqrt{3}}{2}sin2x-\frac{1}{2}cos2x\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{4}+\frac{k\pi}{2}\\sin\left(2x-\frac{\pi}{6}\right)\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{4}+\frac{k\pi}{2}\\x\ne\frac{\pi}{12}+\frac{k\pi}{2}\end{matrix}\right.\)
2.
\(\left\{{}\begin{matrix}sin\left(x+\frac{\pi}{6}\right)\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-\frac{\pi}{6}+k\pi\\x\ne k2\pi\end{matrix}\right.\)
3.
\(sin4x\ne-1\Leftrightarrow4x\ne-\frac{\pi}{2}+k2\pi\)
\(\Leftrightarrow x\ne-\frac{\pi}{8}+\frac{k\pi}{2}\)
36.
\(sin^2x-cos^2x\ne0\Leftrightarrow cos2x\ne0\)
\(\Leftrightarrow x\ne\frac{\pi}{4}+\frac{k\pi}{2}\)
37.
\(cos3x\ne cosx\Leftrightarrow\left\{{}\begin{matrix}3x\ne x+k2\pi\\3x\ne-x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\x\ne\frac{k\pi}{2}\end{matrix}\right.\) \(\Leftrightarrow x\ne\frac{k\pi}{2}\)
38.
\(\left\{{}\begin{matrix}x\ge0\\sin\pi x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\pi x\ne k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne k\end{matrix}\right.\)
39.
\(\left\{{}\begin{matrix}cos\left(x-\frac{\pi}{3}\right)\ne0\\tan\left(x-\frac{\pi}{3}\right)\ne-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x-\frac{\pi}{3}\ne\frac{\pi}{2}+k\pi\\x-\frac{\pi}{3}\ne-\frac{\pi}{4}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{5\pi}{6}+k\pi\\x\ne-\frac{\pi}{12}+k\pi\end{matrix}\right.\)
33.
\(\left\{{}\begin{matrix}cosx\ne0\\cos\frac{x}{2}\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{2}+k\pi\\x\ne\pi+k2\pi\end{matrix}\right.\)
34.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\cotx\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin2x\ne0\\cotx\ne1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\x\ne\frac{\pi}{4}+k\pi\end{matrix}\right.\)
35.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow sinx\ne0\)
\(\Leftrightarrow x\ne k\pi\)
1.
ĐKXĐ: \(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\end{matrix}\right.\) \(\Leftrightarrow sinx.cosx\ne0\)
\(\Leftrightarrow sin2x\ne0\Leftrightarrow x\ne\frac{k\pi}{2}\)
2.
ĐKXĐ: \(\left\{{}\begin{matrix}sinx\ne0\\sin3x\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\x\ne\frac{\pi}{6}+\frac{k2\pi}{3}\end{matrix}\right.\)
3.
Do \(sin6x< 2\) với mọi x nên hàm số xác định trên R
4.
Hàm số xác định khi và chỉ khi \(cosx\ge1\Leftrightarrow cosx=1\)
\(\Leftrightarrow x=k2\pi\)
Đáp án A
Do \(-1\le cosx\le1\Rightarrow\left\{{}\begin{matrix}2+cosx>0\\2-cosx>0\end{matrix}\right.\)
\(\Rightarrow\frac{2+cosx}{2-cosx}>0\) \(\forall x\in R\)