Câu 1: \(y=\cot \left({2x-\dfrac{\pi}{3}}\right)+\tan\left({3x+2019}\right)\) ĐK: \(\left\{ \begin{array}{l} \sin \left({2x-\dfrac{\pi}{3}}\right)\ne0 \\ \cos\left({3x+2019}\right) \ne0\end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} 2x-\dfrac{\pi}{3}\ne k\pi \\ 3x+2019\ne\dfrac{\pi}{2}+k\pi\end{array} \right .\) \(\Leftrightarrow \left\{ \begin{array}{l} x\ne\dfrac{\pi}{6}+ k\dfrac{\pi}{2} \\ x\ne-673+\dfrac{\pi}{6}+k\dfrac{\pi}{3}\end{array} \right .\)\((k\in\mathbb Z)\) Câu 2: \(y={\sin}^2x+2{\cos}^2x+4\cos x-7\) Câu 3:a) \(\sin\left({2x-\dfrac{2\pi}{3}}\right)=\sin\left({3x-\dfrac{\pi}{3}}\right)\) \(\Rightarrow \left[ \begin{array}{l} 2x-\dfrac{2\pi}{3}=3x-\dfrac{\pi}{3}+k2\pi \\ 2x-\dfrac{2\pi}{3}=\pi-\left({3x-\dfrac{\pi}{3}}\right)+k2\pi \end{array} \right .\) \(\Rightarrow \left[ \begin{array}{l} x=-\dfrac{\pi}{3}+k2\pi \\x=\dfrac{2\pi}{5}+k\dfrac{2\pi}{5} \end{array} \right .\)\((k\in\mathbb Z)\) b) ĐK: \(\cos \left({\dfrac{4}{5}}x-30^o\right)\ne0\Rightarrow \dfrac{4}{5}x-30^o\ne\dfrac{\pi}{2}+k\pi\) \(\Rightarrow x\ne\dfrac{5\pi}{6}+k\dfrac{5\pi}{4}\) Phương trình \(\Rightarrow \left[ \begin{array}{l} \sin \left({\dfrac{4}{5}}x-30^o\right)=0 \\ \cos(2x-150^o)=0 \end{array} \right .\) \(\Rightarrow \left[ \begin{array}{l} \dfrac{4}{5}x-30^o=k\pi \\ 2x-150^o=\dfrac{\pi}{2}+k\pi \end{array} \right .\Rightarrow \left[ \begin{array}{l} x=\dfrac{5\pi}{24}+k\dfrac{5\pi}{4} \\ x=\dfrac{2\pi}{3}+k\dfrac{\pi}{2} \end{array} \right .\)(\(k\in\mathbb Z\))