`~rai~`

\(b)\sqrt{3}cosx+sinx=-\sqrt{2}\\\Leftrightarrow \dfrac{\sqrt{3}}{2}cosx+\dfrac{1}{2}sinx=-\dfrac{\sqrt{2}}{2}\\\Leftrightarrow sin\dfrac{\pi}{3}cosx+cos\dfrac{\pi}{3}sinx=-\dfrac{\sqrt{2}}{2}\\\Leftrightarrow sin\left(x+\dfrac{\pi}{3}\right)=-\dfrac{\sqrt{2}}{2}\\\Leftrightarrow \left[\begin{array}{I}x+\dfrac{\pi}{3}=-\dfrac{\pi}{4}+k2\pi\\x+\dfrac{\pi}{3}=\pi-\left(-\dfrac{\pi}{4}\right)+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=-\dfrac{7\pi}{12}+k2\pi\\x=\dfrac{11\pi}{12}+k2\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy phương trình có các họ nghiệm là:}x=-\dfrac{7\pi}{12}+k2\pi;x=\dfrac{11\pi}{12}+k2\pi.(k\in\mathbb{Z})\\d)2sinx-9cosx=\sqrt{85}\\\Leftrightarrow \dfrac{2}{\sqrt{85}}sinx-\dfrac{9}{\sqrt{85}}cosx=1 \\\Leftrightarrow cos\left[arccos\left(\dfrac{2}{\sqrt{85}}\right)\right]sinx-sin\left[arcsin\left(\dfrac{9}{\sqrt{85}}\right)\right]cosx=1\\\Leftrightarrow sin\left(x-arcsin\dfrac{9}{\sqrt{85}}\right)=1\\\Leftrightarrow x-\arcsin\dfrac{9}{\sqrt{85}}=\dfrac{\pi}{2}+k2\pi\\\Leftrightarrow x=\dfrac{\pi}{2}+arcsin\dfrac{9}{\sqrt{85}}+k2\pi.(k\in\mathbb{Z})\\\text{Vậy phương trình có họ nghiệm là:}x=\dfrac{\pi}{2}+arcsin\dfrac{9}{\sqrt{85}}+k2\pi.(k\in\mathbb{Z})\\f)2cosx-3sinx+2=0\\\Leftrightarrow \dfrac{2}{\sqrt{13}}cosx-\dfrac{3}{\sqrt{13}}sinx=-\dfrac{2}{\sqrt{13}}\\\Leftrightarrow cos\left[arccos\left(\dfrac{2}{\sqrt{13}}\right)\right]cosx-sin\left[arcsin\left(\dfrac{3}{\sqrt{13}}\right)\right]sinx=-\dfrac{2}{\sqrt{13}}\\\Leftrightarrow cos\left(x+arccos\dfrac{2}{\sqrt{13}}\right)=-\dfrac{2}{\sqrt{13}}\\\Leftrightarrow \left[\begin{array}{I}x+arccos\dfrac{2}{\sqrt{13}}=arccos\left(-\dfrac{2}{\sqrt{13}}\right)+k2\pi\\x+arccos\dfrac{2}{\sqrt{13}}=-arccos\left(-\dfrac{-2}{\sqrt{13}}\right)+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=arccos\left(-\dfrac{2}{\sqrt{13}}\right)-arccos\dfrac{2}{\sqrt{13}}+k2\pi\\x=-arccos\left(-\dfrac{2}{\sqrt{13}}\right)-arccos\dfrac{2}{\sqrt{13}}+k2\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy phương trình có các họ nghiệm là:}x=arccos\left(-\dfrac{2}{\sqrt{13}}\right)-arccos\dfrac{2}{\sqrt{13}}+k2\pi;\\x=-arccos\left(-\dfrac{2}{\sqrt{13}}\right)-arccos\dfrac{2}{\sqrt{13}}+k2\pi.(k\in\mathbb{Z})\)