Factor each trigonometric expression.
sin³ α + cos³ α

Question

Factor each trigonometric expression.

sin³ α + cos³ α

Accepted Answer

Welcome back. I am so glad you're here. We are asked to rewrite the following trigonometric expression by factoring it completely. Our given expression is the C can't cubed of X plus the tangent cubed of X. Our answer choices are answer choice. A, the quantity of C can't X plus tangent X multiplied by the quantity of C can't squared X minus C can't X tangent X plus tangent squared X. Answer choice B, the quantity of C can't X minus tangent X multiplied by the quantity of C can't squared X minus C can't X tangent X plus tangent squared X. Answer choice C, the quantity of C can't X plus tangent X multiplied by the quantity of C can't squared X plus C can't X tangent X plus tangent squared X. And answer choice D, the quantity of C can't X minus tangent X multiplied by the quantity of C can't squared X plus C can't X tangent X plus tangent squared X. All right. So we take a look at our given trigonometric expression and we recognize that we have a sum of cubes. That's when you have something being cubed added to something else being cubed. So what do we have being cubed here? Well, we see that we have C can't of X being cute plus tangent of X being cubed. And we recall from previous lessons that when we have a sum of cubes, we have a cubed plus B cubed that is equal to the factored out the quantity of A plus B multiplied by the quantity of A squared minus A B plus B squared. And now all we have to do is identify A and B and plug those in and we have it factored. So we said already that A, the first thing being cubed is going to be the C can't of X and B. The second thing being cubed is the tangent of X. So we just need to plug in for A and B in our factored form. So first, we have the quantity of A is C can't X plus B is tangent X multiplied by the quantity of A squared. So that's C can't squared X minus A multiplied by B. So A is C can't X multiplied by B is tangent X and then that's going to be plus B squared B is tangent X. So that's tangent squared and we're just about out of room on the screen. So I'm gonna scoot this over tangent squared X and there we have it fully factored. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Factor each trigonometric expression.
sin³ α + cos³ α

Key Concepts

Sum of Cubes Formula

Trigonometric Identities

Factoring Techniques

Watch next

Factor each trigonometric expression.sin³ α + cos³ α

Key Concepts

Sum of Cubes Formula

Trigonometric Identities

Factoring Techniques

Watch next

Factor each trigonometric expression.
sin³ α + cos³ α