# Question Video: Simplifying Trigonometric Expressions Using Pythagorean and Reciprocal Identities Mathematics • 10th Grade

Simplify sin π csc π β cosΒ² π.

01:39

### Video Transcript

Simplify sin π multiplied by csc π minus cos squared π.

In this question, we are asked to simplify a trigonometric expression. One way of doing this is using the reciprocal and Pythagorean identities. In questions of this type, it is not always clear what to do first. However, as a general rule, it is worth replacing any reciprocal functions with the sine, cosine, or tangent function.

We know that csc π is equal to one over sin π. Substituting this into our expression, we have sin π multiplied by one over sin π minus cos squared π. The sin π on the numerator and denominator of our first term cancels, leaving us with one minus cos squared π. Next, we recall one of the Pythagorean identities: sin squared π plus cos squared π is equal to one. Subtracting cos squared π from both sides, this can be rewritten as sin squared π is equal to one minus cos squared π. This means that our expression can be rewritten as sin squared π. sin π multiplied by csc π minus cos squared π written in its simplest form is sin squared π.