Question

Which expression is equal to csc x, written in termsof cos x ?

Answer 1

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