Question

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

Answer 1

`x=\p \pi n ,x=(3\pi)/(2) \pm 2\pi n`

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=(\pi)/(2)`

In the third quadrant,

`x=\pi +(\pi)/(2)`

`x=(3\pi)/(2)`

In the fourth quadrant,

`x=2\pi -(\pi)/(2)`

`x=(3\pi)/(2)`

This is a repeated solution.

So the general solution is

If
`sin x=-1`, then
`x=(3\pi)/(2)\pm 2\pi n`

Putting the two solutions together gives

`x=\pm \pi n ,x=(3\pi)/(2) \pm 2\pi n`, where n is an integer

The correct answer is C.