Question

Help please!
Rewrite with only sin x and cos x.
cos 3x

Answer 1

here is a start
cos(3x)=cos(2x+x)

Answer 2

I would first use sum identity for cosine to expand that

Answer 3

then I would end up using the double angle identity later on

Answer 4

I know we can apply the Angle Addition Formula for Cosine.
cos(2x+x) = cos(2x)cosx - sin(2x)sinx
And then apply the Cosine Double Angle Formula to the cos(2x)and the Sine Double Angle Formula to the sin(2x)
Which is = (cos^2 x- sin^2 x) cos x - (2sin x cos x) sin x, but I am stuck on how to simplify it down from here.

Answer 5

so you have
\[\cos(3x) \\ \cos(2x+x) \\ \cos(2x)\cos(x)-\sin(2x)\sin(x) \\ (\cos^2(x)-\sin^2(x))\cos(x)-2\sin(x)\cos(x) \sin(x) \\ \text{ distribute } \\ \cos^3(x)-\sin^2(x)\cos(x)-2\sin(x)\cos(x)\sin(x) \\ \cos^3(x)-\sin^2(x)\cos(x)-2\sin^2(x)\cos(x)\]

Answer 6

you can combine like terms

Answer 7

@pansycamel you cool with that?

Answer 8

combining the like terms part?

Answer 9

2 sin^2 x cos - 2 sin x cos x?

Answer 10

wait how did you get that?

Answer 11

A. cos x - 4 cos x sin^2 x B. -sin^3x + 2 sin x cos x C. -sin^2x + 2 sin x cos x
D. 2 sin^2x cos x - 2 sin x cos x . These are my answer choices, I think i am having trouble combining the like terms

Answer 12

@jim_thompson5910 , any help?

Answer 13

do you understand freckles' steps?

Answer 14

Freckles expanded the equation. I am a little confused still.

Answer 15

can you simplify \(\cos^3(x)-\sin^2(x)\cos(x)-2\sin^2(x)\cos(x)\) any further?

Answer 16

When I try I get 4 cos^3 (x) - 3 cos x but that isn't one of the choices

Answer 17

factor out a cos(x)

Answer 18

then use the idea cos^2 = 1 - sin^2

Answer 19

Wait, cos(x) - 4 sin^2 (x) cos (x) is an answer though. Thank you:)

Answer 20

yes you got it