Question

Solve sin(x)(sinx +1) = 0

Answer 1

Answer:

$x=\p \pi n ,x=\frac{3\pi}{2} \pm 2\pi n$

Step-by-step explanation:

We want to solve the equation,

$sinx(sin x+1)=0$

By the zero product property of multiplication,

$sinx=0\:or\:(sin x+1)=0$

$\Rightarrow sinx=0\:or\:sin x=-1$

If $sinx=0$, then, $x=\pi$

The general solution is

$x=\pm \pi n$

For $sinx=-1$, it means $x$ is either in the third quadrant or fourth quadrant.

So we first solve for,

$sinx=1$

This implies that,

$x=\frac{\pi}{2}$

In the third quadrant,

$x=\pi +\frac{\pi}{2}$

$x=\frac{3\pi}{2}$

In the fourth quadrant,

$x=2\pi -\frac{\pi}{2}$

$x=\frac{3\pi}{2}$

This is a repeated solution.

So the general solution is

If $sin x=-1$, then $x=\frac{3\pi}{2}\pm 2\pi n$

Putting the two solutions together gives

$x=\pm \pi n ,x=\frac{3\pi}{2} \pm 2\pi n$, where n is an integer

The correct answer is C.