Answer:
See Below.
Explanation:
We want to verify the equation:

We can convert sec(α) to 1 / cos(α):

Multiply both layers of the first fraction by cos(α):

Create a common denominator. We can multiply the first fraction by (1 - cos(α)):

Simplify:

From the Pythagorean Identity, we know that cos²(α) + sin²(α) = 1 or equivalently, 1 - cos²(α) = sin²(α). Substitute:

Subtract:

Distribute:

Rewrite:

Split:

Factor the second fraction, and substitute sin²(α) for 1 - cos²(α):

Factor:

Cancel:

Divide the second fraction by cos(α):

Hence proven.