Question

Prove: cos θ - cos θ•sin2 θ = cos3 θ. You must show all work.

Answer 1

@mathissuperhard23

Answer 2

@calculusxy

Answer 3

Hey, I might be able to help. I haven't done these in a while though so it might take some trial and error.

Answer 4

Have you tried proving it already?

Answer 5

yes i have but i can't seem to get it

Answer 6

Ok, I will give it a try

Answer 7

thank you so much

Answer 8

Is cosx - (cosx)(sin2x) = cos3x correct? I just want to make sure nothing is missing

Answer 9

I don't believe they are equal

Answer 10

Okay I see what has happened. I thought it was cos(3x) but it is actually (cosx)^3

Answer 11

Okay I can help you now. We should start with the left side because it is more complicated. Lets start by factoring out cosx

Answer 12

You will then be left with cosx(1-sin^2(x)) and we know from our pythagorean identities that sin^2(x) + cos^2(x) =1 can be arranged to form 1-sin^2(x)=cos^2(x)

Answer 13

So sub cos^2(x) for (1-sin^2(x)) and you will be left with cosx(cos^2(x)) which we can see will simplify to cos^3(x), proving the equation!