I know the answer to this question but I don't know how to prove it.

Question

Simplify (sec(x) - cos(x))/tan²x

1. simplify using trigonometry identities

Answer 1

Using the identities:

1) sec(x) = 1/cos(x)

2) tan(x) = sin(x)/cos(x) therefore tan²(x) = sin²(x)/cos²(x)

3) sin²(x) + cos²(x) = 1 or sin²(x) = 1 - cos²(x)