# Video: Simplifying Trigonometric Expressions Using Reciprocal Identities

Simplify cosΒ² π sec π csc π.

01:28

### Video Transcript

Simplify cos squared π times sec π times csc π.

Using some trig identities, we can replace a few of these things and maybe have some things cancel and then we can simplify. So we know that the sec π is equal to one over cos π, and then csc π is equal to one over sin π. So by replacing those, the cosine on the denominator will cancel with one of the cosines on the numerator. Since itβs cosine squared, thatβs the same as having two cosines.

So on the numerator, we have cosine times one times one, so we have cos π, and then on the bottom, thereβs only a sin of π. Now this does simplify a little bit more. The reason why is because cosine divided by sine has a relationship because if we would flip that sin of π divided by cos of π, that is equal to tan of π; it simplifies.

Now we could write that as tan of π over one, so that means that if we would flip that upside down, it would be equal to what we had: cos of π divided by sin of π. So we have one divided by the tan of π, and we actually know what that is. One divided by the tan of π is equal to the cot of π. So after simplifying, our final answer would be cot of π.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.