ANSWER
x = 0°, 180°, 210°, 330°
EXPLANATION
We have to find x when both functions have the same value,
[tex]2\sin ^2x=-\sin x[/tex]
Add sin(x) to both sides,
[tex]2\sin ^2x+\sin x=0[/tex]
And we have a quadratic equation, where the variable is sin(x). Factor out 2 sin(x),
[tex]2\sin x(\sin x+\frac{1}{2})=0[/tex]
The solutions are,
[tex]\begin{cases}\sin x=0 \\ \\ \sin x=-\frac{1}{2}\end{cases}[/tex]
Now we have to find the values of x whose sine is 0 and the ones whose sine is -1/2,
[tex]\begin{gathered} \sin x=0\Rightarrow x=0\degree;x=180\degree \\ \\ \sin x=-\frac{1}{2}\Rightarrow x=210\degree;x=330\degree \end{gathered}[/tex]
Hence, the values where they are the same are 0°, 180°, 210° and 330°
