Verifying an identity by multiplying by sine

The video tutorial explains how to verify a trigonometric identity by simplifying expressions. Initially, the teacher considers using conjugate multiplication but finds it unhelpful. Instead, the focus shifts to using the reciprocal relationship between sine and cosecant. By multiplying the expression by sine over sine, the teacher demonstrates how to create an equivalent fraction without changing its value. This approach simplifies the left side to match the right side, successfully verifying the identity.

What does the speaker mean by saying that multiplying by sine over sine does not change the value of the rational expression?

Describe the final outcome of the verification process as mentioned in the text.