$\begin{array}{l}c)\,\,2\cos x - \sin x = 0\\ +) \quad \cos x = 0\Rightarrow \sin x = 0 \quad (loại)\quad \text{(cos x và sin x không đồng thời bằng 0)}\\ +) \quad \cos x \ne 0\Rightarrow \tan x = 2\Leftrightarrow x = \arctan2 + k\pi \quad (k \in\Bbb Z)\\ d)\,\,\sin7x - \cos x = \sin x + \cos7x\\ \Leftrightarrow \sin7x - \cos7x = \sin x + \cos x\\ \Leftrightarrow \sin\left(7x - \dfrac{\pi}{4}\right) = \sin\left(x + \dfrac{\pi}{4}\right)\\ \Leftrightarrow \left[\begin{array}{l} 7x - \dfrac{\pi}{4} = x+ \dfrac{\pi}{4} + k2\pi\\7x - \dfrac{\pi}{4} = \dfrac{3\pi}{4} - x + k2\pi\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l} 6x =\dfrac{\pi}{2} + k2\pi\\8x =\pi + k2\pi\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l} x =\dfrac{\pi}{12} + k\dfrac{\pi}{3}\\x =\dfrac{\pi}{8} + k\dfrac{\pi}{4}\end{array}\right.\quad (k \in \Bbb Z) \end{array}$
