How to simplify a trigonometric expression by adding two expressions

The video tutorial focuses on simplifying mathematical expressions by using identities. It begins with the goal of simplifying an expression into one form, identifying the use of addition, and recognizing that the terms are not like terms. The instructor suggests using reciprocal identities to rewrite the expression in terms of sines and cosines. The process involves rewriting, combining like terms, and simplifying fractions to achieve a final expression in terms of secant. The tutorial concludes with a reminder to simplify expressions fully.

Why does the teacher choose not to use the Pythagorean identities in this case?

What does the teacher mean by 'common terms' in the context of simplifying the expression?