Simplify by combining two rational trigonometric expressions

The video tutorial explains how to simplify a complex trigonometric expression involving sine cubed and cotangent squared. It begins by finding a common denominator, then uses reciprocal identities to simplify the expression. The Pythagorean identity is applied to further simplify, leading to the final expression in terms of cosecant.

What is the common denominator when subtracting sine cubed of X and cotangent squared of X divided by sine of X?

How can you rewrite cotangent squared of X in terms of sine and cosine?

What identity can be used to simplify 1 minus cosine squared of X?

Explain how sine squared of X divided by sine cubed of X simplifies to one over sine of X.

What is the final simplified expression for the operation described in the text?