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:

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

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

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

a: ĐKXĐ: 2*sin x+1<>0

=>sin x<>-1/2

=>x<>-pi/6+k2pi và x<>7/6pi+k2pi

b: ĐKXĐ: \(\dfrac{1+cosx}{2-cosx}>=0\)

mà 1+cosx>=0

nên 2-cosx>=0

=>cosx<=2(luôn đúng)

c ĐKXĐ: tan x>0

=>kpi<x<pi/2+kpi

d: ĐKXĐ: \(2\cdot cos\left(x-\dfrac{pi}{4}\right)-1< >0\)

=>cos(x-pi/4)<>1/2

=>x-pi/4<>pi/3+k2pi và x-pi/4<>-pi/3+k2pi

=>x<>7/12pi+k2pi và x<>-pi/12+k2pi

e: ĐKXĐ: x-pi/3<>pi/2+kpi và x+pi/4<>kpi

=>x<>5/6pi+kpi và x<>kpi-pi/4

f: ĐKXĐ: cos^2x-sin^2x<>0

=>cos2x<>0

=>2x<>pi/2+kpi

=>x<>pi/4+kpi/2

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