One of the difficulties associated with understanding how to verify a trigonometric Identity is that the teacher, professor, or instructor often leaves out steps that he considers trivial or easy. Verifying a trig identity is a type of proof and may bring back the bad memories associated with geometry proofs.
Establishing a trig identity almost always involve much more algebra than trigonometry. The concepts involved proving the following trig identity are finding a common denominator, adding the numerators of the two fractions with like denominators, factoring the numerator, using one of the Pythagorean Identities, and finally noting that the reciprocal of the cosine function is the secant function.
I hope you understand and enjoy the verification of the following trig Identity.