If the general solution of  $\sin x+3\sin 3x+\sin 5x=0$ is $x=y$  then the set of all values of  $\cos y$  is

 $$\begin{gathered} \sin x+\sin 5x+3\sin 3x=0 \\ \Rightarrow 2\sin 3x\cos 2x+3\sin 3x=0 \\ \Rightarrow \sin 3x[2\cos 2x+3]=0\Rightarrow \sin 3x=0 \\ \Rightarrow x=0,\pi \\ so , y=0,\pi \Rightarrow \cos 0=1 \\ \Rightarrow \cos \pi =-1 \\ and \cos 2x=-\frac{3}{2} \\ \Rightarrow 2{\cos }^{2}x-1=|-\frac{3}{2}| \\ \Rightarrow 2{\cos }^{2}x=1-\frac{3}{2} \\ \Rightarrow {\cos }^{2}x=\frac{1}{4} \\ \Rightarrow \cos x=\pm \frac{1}{2} \\ \Rightarrow \cos y=1,-1,\frac{1}{2},-\frac{1}{2} \end{gathered}$$