1.

ĐKXĐ: \(\left\{{}\begin{matrix}cosx\ne0\\tanx-sinx\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}cosx\ne0\\\dfrac{sinx}{cosx}-sinx\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}cosx\ne0\\sinx\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow sin2x\ne0\Leftrightarrow x\ne\dfrac{k\pi}{2}\)

2.

ĐKXĐ: \(sin2x\ne0\Leftrightarrow x\ne\dfrac{k\pi}{2}\)

3. 

ĐKXĐ: \(\left\{{}\begin{matrix}sin\left(x-\dfrac{\pi}{4}\right)\ne0\\cos\left(x-\dfrac{\pi}{4}\right)\ne0\end{matrix}\right.\)

\(\Leftrightarrow sin\left(2x-\dfrac{\pi}{2}\right)\ne0\Leftrightarrow cos2x\ne0\)

\(\Leftrightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

câu 2 ..... \(\dfrac{cos^22x}{sin^22x}=cot^22x\) nên suy ra sin2x khác 0 đúng hơm

còn câu 3, tui ko hiểu chỗ sin(2x-pi/4).. sao ở đây rớt xuống dợ

a.

\(\left\{{}\begin{matrix}sin\left(3x+\dfrac{\pi}{6}\right)\ne0\\cos2x\ne0\\sinx\ne-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-\dfrac{\pi}{18}+\dfrac{k\pi}{3}\\x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x\ne-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)

b.

Do \(5+2cot^2x-sinx=4+2cot^2x+\left(1-sinx\right)>0\) nên hàm xác định khi:

\(\left\{{}\begin{matrix}sinx\ne0\\sin\left(x+\dfrac{\pi}{2}\right)\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\end{matrix}\right.\) \(\Leftrightarrow sin2x\ne0\)

\(\Leftrightarrow x\ne\dfrac{k\pi}{2}\)

ĐKXĐ:

a.

\(sin5x\ne0\Leftrightarrow5x\ne k\pi\Rightarrow x\ne\dfrac{k\pi}{5}\)

b.

\(cos6x\ne0\Leftrightarrow6x\ne\dfrac{\pi}{2}+k\pi\Rightarrow x\ne\dfrac{\pi}{12}+\dfrac{k\pi}{6}\)

d.

\(sin\left(3x-\dfrac{\pi}{6}\right)\ne0\Leftrightarrow3x-\dfrac{\pi}{6}\ne k\pi\Rightarrow x\ne\dfrac{\pi}{18}+\dfrac{k\pi}{3}\)

e.

\(sin\left(4x-\dfrac{\pi}{3}\right)\ne0\Leftrightarrow4x-\dfrac{\pi}{3}\ne k\pi\Rightarrow x\ne\dfrac{\pi}{12}+\dfrac{k\pi}{4}\)

1:

a: ĐKXĐ: \(x< >\dfrac{\Omega}{2}+k\Omega\)

=>TXĐ: \(D=R\backslash\left\{\dfrac{\Omega}{2}+k\Omega\right\}\)

b: ĐKXĐ: \(x< >k\Omega\)

=>TXĐ: \(D=R\backslash\left\{k\Omega\right\}\)

c: ĐKXĐ: \(2x< >\dfrac{\Omega}{2}+k\Omega\)

=>\(x< >\dfrac{\Omega}{4}+\dfrac{k\Omega}{2}\)

TXĐ: \(D=R\backslash\left\{\dfrac{\Omega}{4}+\dfrac{k\Omega}{2}\right\}\)

d: ĐKXĐ: \(3x< >\Omega\cdot k\)

=>\(x< >\dfrac{k\Omega}{3}\)

TXĐ: \(D=R\backslash\left\{\dfrac{k\Omega}{3}\right\}\)

e: ĐKXĐ: \(x+\dfrac{\Omega}{3}< >\dfrac{\Omega}{2}+k\Omega\)

=>\(x< >\dfrac{\Omega}{6}+k\Omega\)

TXĐ: \(D=R\backslash\left\{\dfrac{\Omega}{6}+k\Omega\right\}\)

f: ĐKXĐ: \(x-\dfrac{\Omega}{6}< >\Omega\cdot k\)

=>\(x< >k\Omega+\dfrac{\Omega}{6}\)

TXĐ: \(D=R\backslash\left\{k\Omega+\dfrac{\Omega}{6}\right\}\)

1. \(sin\left(\dfrac{\pi}{3}-x\right)\ne0\Leftrightarrow\dfrac{\pi}{3}-x\ne k\pi\Leftrightarrow x\ne\dfrac{\pi}{3}-k\pi\)

2. \(cos2x\ne0\Leftrightarrow2x\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

3. \(\sqrt{1+sinx}-\sqrt{2}\ge0\Leftrightarrow1+sinx\ge2\Leftrightarrow sinx\ge1\Leftrightarrow sinx=1\Leftrightarrow x=\dfrac{\pi}{2}+k2\pi\)

4. \(\sqrt{2-2cosx}-2\ne0\Leftrightarrow2-2cosx\ne4\Leftrightarrow cosx\ne-1\Leftrightarrow x\ne\pi+k2\pi\)

5. \(1-\sqrt{1+sin3x}\ne0\Leftrightarrow sin3x\ne0\Leftrightarrow3x\ne k\pi\Leftrightarrow x\ne\dfrac{k\pi}{3}\)

1. \(D=R\)

2. \(sinx\ne0\Leftrightarrow x\ne k\pi\Rightarrow D=R\backslash\left\{k\pi|k\in R\right\}\)

3. \(cos2x\ne0\Leftrightarrow2x\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\Rightarrow D=R\backslash\left\{\dfrac{\pi}{4}+\dfrac{k\pi}{2}|k\in R\right\}\)

4. \(cos\left(x+\dfrac{\pi}{4}\right)\ne0\Leftrightarrow x+\dfrac{\pi}{4}\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+k\pi\Rightarrow D=R\backslash\left\{\dfrac{\pi}{4}+k\pi|k\in R\right\}\)