Answer:
[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]
Step-by-step explanation:
The given trigonometric equation is;
[tex]\sin x(\sin x-1)=0[/tex]
By the zero product property;
[tex]\sin x=0[/tex] or [tex]\sin x-1=0[/tex]
For [tex]\sin x=0[/tex], the general solution is [tex]x=n \pi[/tex]
[tex]\sin x-1=0[/tex], [tex]\sin x=1[/tex], the general solution is [tex]x=2\pi n+\frac{\pi}{2}[/tex]
Therefore the general solution is:
[tex]x=n \pi[/tex] or [tex]x=2\pi n+\frac{\pi}{2}[/tex]
