Simplify a trigonometric expression and then find the sum

The video tutorial explains how to simplify a trigonometric expression involving X divided by the cosecant of X plus cosine squared of X. The instructor demonstrates rewriting the expression in terms of sines and cosines, applying reciprocal identities, and ultimately using the Pythagorean identity to simplify the expression to 1.

What happens when you multiply by the reciprocal of sine of X?

Why is it important to remember the Pythagorean identity in trigonometry?