Two trig identities are of interest here:
... sin(x)² + cos(x)² = 1
... csc(x) = 1/sin(x)
Using the first one, you can subtract cos(x)², the take the square root to find
... sin(x) = ±√(1 - cos(x)²)
Using that in the second one, you have
... csc(x) = ±1/√(1 - cos(x)²) . . . . . . . . . . . . . matches the 3rd choice
