Select all values x in the range of arc sint which satisfy s

Select all values x in the range of arc sin(t) which satisfy sin^2 (x) + 4 sin (x) + 4 = 0. - pi /2 There are no solutions. 3 pi /2 -3 pi /2 pi /2

Let sinx = y

We have
y^2 + 4y + 4 = 0

This is a quadratic, wich can be factored as :
(y+ 2)(y + 2) = 0

So, solution is :
y = -2

We now have :
sinx = -2

We know that range of arcsin(t) is [-pi/2 , pi/2]
But the domain of arcsin(t) is only between [-1 , 1]

Here we have sinx= -2
This is impossible

So, no solutions

Option B