Bài 10

ĐKXĐ: \(\left\{{}\begin{matrix}cos\left(1-x\right)\ne0\\2sin2x.cos2x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}cos\left(1-x\right)\ne0\\sin4x\ne1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}1-x\ne\dfrac{\pi}{2}+k\pi\\4x\ne\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1-\dfrac{\pi}{2}-k\pi\\x\ne\dfrac{\pi}{8}+\dfrac{k\pi}{2}\end{matrix}\right.\left(k\in Z\right)\)

Bài 11.

ĐKXĐ: \(\left\{{}\begin{matrix}cos^2x-sin^2x\ne0\\sin2x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}cos2x\ne0\\sin2x\ne0\end{matrix}\right.\)

\(\Leftrightarrow2x\ne\dfrac{k\pi}{4}\Leftrightarrow x\ne\dfrac{k\pi}{8}\)

Bài 12.

ĐKXĐ: \(\left\{{}\begin{matrix}1-2cos^2x\ne0\\1+tanx\ne0\\cosx\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}cos2x\ne0\\tanx\ne-1\\cosx\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne\dfrac{\pi}{2}+k\pi\\x\ne-\dfrac{\pi}{4}+k\pi\\x\ne\dfrac{\pi}{2}+k\pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x\ne-\dfrac{\pi}{4}+k\pi\\x\ne\dfrac{\pi}{2}+k\pi\end{matrix}\right.\left(k\in Z\right)\)

Bài 10: 

ĐKXĐ của hàm số \(y=\dfrac{tan\left(1-x\right)+2}{2sin2xcos2x-1}\) là: 

\(\left\{{}\begin{matrix}1-x\ne\dfrac{\pi}{2}+k\pi\\2sin2xcos2x-1\ne0\end{matrix}\right.,k\inℤ\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne1-\dfrac{\pi}{2}+k\pi\\sin4x\ne1\end{matrix}\right.,k\inℤ}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne1-\dfrac{\pi}{2}+k\pi\\4x\ne\dfrac{\pi}{2}+k2\pi\end{matrix}\right.,k\inℤ\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne1-\dfrac{\pi}{2}+k\pi\\x\ne\dfrac{\pi}{8}+\dfrac{k\pi}{2}\end{matrix}\right.,k\inℤ\)

Bài 11:

ĐKXĐ của hàm số \(y=\dfrac{sin^22x+1}{cos^2x-sin^2x}+cot^22x\) là: 

\(\left\{{}\begin{matrix}cos^2x-sin^2x\ne0\\2x\ne k\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}cos2x\ne0\\x\ne\dfrac{k\pi}{2},k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne\dfrac{\pi}{2}+k\pi\\x\ne\dfrac{k\pi}{2}\end{matrix}\right.,k\inℤ\)

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

Bài 12: 

ĐKXĐ của hàm số \(y=\dfrac{sinx+1}{\left(1-2cos^2x\right)\left(1+tanx\right)}\) là: 

\(\left\{{}\begin{matrix}1-2cos^2x\ne0\\1+tanx\ne0\\x\ne\dfrac{\pi}{2}+k\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}cos2x\ne0\\tanx\ne-1\\x\ne\dfrac{\pi}{2}+k\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne\dfrac{\pi}{2}+k\pi\\x\ne\dfrac{-\pi}{4}+k\pi\\x\ne\dfrac{\pi}{2}+k\pi\end{matrix}\right.,k\inℤ\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\\x\ne\dfrac{-\pi}{4}+k\pi\\x\ne\dfrac{\pi}{2}+k\pi\end{matrix}\right.,k\inℤ\)

Bài 13: 

ĐKXĐ của hàm số \(y=\dfrac{\sqrt{4-sinx}}{1-cos^2x}+2cot\left(\dfrac{x}{2}-\dfrac{\pi}{6}\right)\) là: 

\(\left\{{}\begin{matrix}4-sinx\ge0\\1-cos^2x\ne0\\\dfrac{x}{2}-\dfrac{\pi}{6}\ne k\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}sinx\ne0\\x\ne\dfrac{\pi}{3}+k2\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\x\ne\dfrac{\pi}{3}+k2\pi\end{matrix}\right.,k\inℤ\)

Bài 14: 

ĐKXĐ của hàm số \(y=\dfrac{3sinx+1}{1+cos^22x}+\dfrac{1-tan\left(3x-2\right)}{3-cos^2x+sin^2x}\) là: 

\(\left\{{}\begin{matrix}1+cos^22x\ne0\\3x-2\ne\dfrac{\pi}{2}+k\pi,k\inℤ\\cos^2x-sin^2x=cos2x\ne3\end{matrix}\right.\)

\(\Leftrightarrow x\ne\dfrac{\pi}{6}+\dfrac{2}{3}+\dfrac{k\pi}{3},k\inℤ\)

Bài 15: 

ĐKXĐ của hàm số \(y=\dfrac{\left(1-2tan3x\right)\left(sinx-1\right)}{sin^4x-cos^4x}\) là: 

\(\left\{{}\begin{matrix}3x\ne\dfrac{\pi}{2}+k\pi,k\inℤ\\sin^4x-cos^4x\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{3},k\inℤ\\sin^2x-cos^2x=-cos2x\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{3},k\inℤ\\2x\ne\dfrac{\pi}{2}+k\pi,k\inℤ\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{3}\\x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\end{matrix}\right.,k\inℤ\)