• # question_answer The equation $|\sin \,x|\,\,=\sin x+3$ has in$[0,\,\,2\pi ]:$ A) no root B) only one root C) two roots D) more than two roots

 If $\sin \,\,x>0$ $\Rightarrow$ $\sin \,x=\sin \,x+3$$\Rightarrow$ not possible If $\sin \,\,x<0$$\Rightarrow$ $-\sin \,\,x<0$$\Rightarrow$ $-\sin x=\sin x+3=1$ $\sin x=-\,3/2$  not possible