Question

Prove: sin θ - sin θ cos2 θ = sin3 θ. I have to show all work

Answer 1

@ganeshie8 @kc_kennylau @ranga @shamil98 @AriPotta

@ganeshie8 @TuringTest @thomaster

Answer 2

@Tazmann
@ganeshie8 @TuringTest @thomaster
@zimmah

Answer 3

is that \[ \sin \theta - \sin \theta \cos(2\theta) = \sin(3 \theta)\]or \[ \sin \theta - \sin \theta \cos^2\theta = \sin^3 \theta\]or some combination thereof?

Answer 4

I will attach a pic of the question

Answer 5

why couldn't you have just said "the second one you wrote" ?

Answer 6

cos I wasnt sure it was the second one you wrote

Answer 7

just to avoid error

Answer 8

try factoring the left side

Answer 9

how do i do that?

Answer 10

could you factor
x-xy ?

Answer 11

x (1 - y)

Answer 12

?

Answer 13

yes, now let sin(t)=x and cos^2(t)=y and factor it the same way

Answer 14

after you factor out the left side, then use the identity :
sin^2 θ + cos^2 θ = 1

Answer 15

I cant figure it out.

Answer 16

What should me equation look like?

Answer 17

*my

Answer 18

x=sin(t)
y=cos^2(t)
substitute to get
x-xy
factor this, as you showed you are capable of, and substitute back in for x and y

Answer 19

So sin(t) - sin(t)cos^2(t)?

Answer 20

that is still in the form
x-xy
factor this and what do you get?

Answer 21

how do i go about factoring this?

Answer 22

you already did it once above

Answer 23

I said "can you factor x-xy ?"
and you wrote the answer

reread above

Answer 24

so sin(t) (1 - cos(t^2))

Answer 25

almost, but\[\cos^2\theta=(\cos\theta)^2\ne\cos(\theta^2)\]

Answer 26

you have confused the two

Answer 27

I really don't get it. can you factor it for me?

Answer 28

you factored it fine, but there never was a cos(t^2) in your problem

Answer 29

there is a difference between cos^2(t) and cos(t^2), you need to understand that

Answer 30

yeah but i don't know how to factor it when cos^2(t)

Answer 31

I just told you twice how to factor it, and you did factor it, and then, for some reason I don't understand, you changed cos^2(t) to cos(t^2)
aside from that it's fine so far

Answer 32

You can't just keep on telling me how to factor it if i don't know how!
x-xy is one thing, that problem is quite another

Answer 33

actually they are identical
x=sin(t)
y=cos^2(t)
now we can forget what x and y stand for and substitute, giving
x-xy=x(1-y)
now just make the *exact* same substitution in reverse to go back to sin and cos