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

Simplify sin 𝜃 csc 𝜃 − cos² 𝜃.

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### Video Transcript

Simplify sin 𝜃 multiplied by csc 𝜃 minus cos squared 𝜃.

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