Question

Answer 1

1) Nhận xét: \(1-cosx\ge0\forall x\) ; \(1+sinx\ge0\forall x\)

Hàm số xđ <=> \(\left\{{}\begin{matrix}\dfrac{1-cosx}{1+sinx}\ge0\left(lđ\right)\\1+sinx\ne0\end{matrix}\right.\) \(\Rightarrow sinx\ne-1\) \(\Leftrightarrow x\ne\dfrac{-\pi}{2}+k2\pi\left(k\in Z\right)\)

2) Hàm số xđ <=> \(\left\{{}\begin{matrix}tanx\ne0\\cosx\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\end{matrix}\right.\)\(\Rightarrow sinx.cosx\ne0\) 

\(\Leftrightarrow\dfrac{1}{2}.sin2x\ne0\) \(\Leftrightarrow x\ne\dfrac{k\pi}{2}\left(k\in Z\right)\)

3)Hàm số xđ <=>\(1-sin\left(x^2+2x-1\right)\ge0\)

\(\Leftrightarrow sin\left(x^2+2x-1\right)\le1\) (lđ với mọi x)

Vậy tập xđ là D=R

4)Hàm số xđ <=> \(1-cosx\ne0\) \(\Leftrightarrow cosx\ne1\) \(\Leftrightarrow x\ne k2\pi\left(k\in Z\right)\)

6) Hàm số xđ <=> \(\left\{{}\begin{matrix}sinx\ne0\\cos2x\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\2cos^2x-1\ne0\end{matrix}\right.\)(\(k\in Z\)) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\cosx\ne\pm\sqrt{\dfrac{1}{2}}\end{matrix}\right.\)(\(k\in Z\))

\(\left\{{}\begin{matrix}x\ne k\pi\\x\ne\pm\dfrac{\pi}{4}+k2\pi\\x\ne\pm\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\) (\(k\in Z\))