Mathematics - Trigonometric Equation Question with Solution | TestHub

$$\begin{array}{rl}& \sin 2x-2\cos x+4\sin x=4\\ & \Rightarrow 2\sin x\cdot \cos x-2\cos x+4\sin x-4=0\\ & \Rightarrow (\sin x-1)(\cos x-2)=0\end{array}$$ $$\begin{array}{rl}& \because \cos x-2\ne 0,\therefore \sin x=1\\ & \therefore x=\frac{\pi }{2},\frac{5\pi }{2},\frac{9\pi }{2}\end{array}$$