Question

Emergency help on an Algebra II exam!

Prove: sin θ - sin θ•cos2 θ = sin3 θ. You must show all work.

Answer 1

it looks like this is an exam

Answer 2

It's a practice exam, but it's worth a good bit of points and while I can understand the proofs written out in my lessons, this particular problem is stumping me. I've been working on these tests for hours :(

Answer 3

So I know that identity of sin^2theta + cos^2theta = 1, or...something pretty close to that...

Answer 4

show me the attempts you have made.

Answer 5

Okay. So the sin theta should cancel, right?
cos^2 theta = sin^3 theta ****(that 3 is a cube, not sin(3))****
I don't know what to do with that!

Answer 6

how does it cancel?

Answer 7

Bc it's just subtracted. Like 1 - 1 = 0.

Answer 8

sin theta - sin theta = 0.

Answer 9

no

Answer 10

sin is multiplied to cos
sin θ - (sin θ•cos2 θ) = sin3 θ
ORDERS of operation

Answer 11

Parentheses first, then

Answer 12

btw, is that \(cos^2 \theta \) or \(cos (2 \theta) \)

Answer 13

The first, it's squared.

Answer 14

Okay, so...then do we distribute the negative into the parentheses??

Answer 15

I'm thinking maybe we subtract sin theta from both sides to give us (sin theta * cos^2 theta) = sin^2 theta

Answer 16

is that \(sin^3 \theta \) or \(sin (3 \theta) \)

Answer 17

Cubed, the first one.

Answer 18

you need to start typing these things appropriately because they mean different things

Answer 19

I'm sorry, I didn't realize it before I posted bc I just copy and pasted it to preserve the theta symbols :(

Answer 20

like this?
PROVE
\(sin ~\theta - (sin~ \theta ~cos^2 \theta) = sin^3 \theta \)

Answer 21

There weren't any parentheses, but otherwise, yes.

Answer 22

so tell me what should be the best identity we can use?

Answer 23

The only one I know of is the one I typed above, the sin^2 theta + cos^2 theta = 1.

Answer 24

We didn't focus a lot on identities, so I suppose I may be forgetting some, but they aren't in my notes =/

Answer 25

what did you focus on?

Answer 26

let us use trigonometric expansion and make use of some algebra techniques like factoring, yes?

Answer 27

do you think you can factor the left-hand-side (LHS) of the equation for me?

Answer 28

Sorry! Lost connection!

Answer 29

I can tryyy, hold on