Question

Help please!

Rewrite with only sin x and cos x.

cos 3x

Answer 1

Use the FORMULA
sin 3x = 3sin x - 4 (sin x)^3
cos 3x = 4 (cos x)^3 - 3 cos x

sin 3x + cos 3x
= 3sin x - 4 (sin x)^3 + 4 (cos x)^3 - 3 cos x

And this is how the FORMULA comes...

sin 3x
= sin (x + 2x)
= sin x cos 2x + cos x sin 2x
= sin x (1 - 2 (sin x)^2) + 2 sin x (cos x)^2
= sin x - 2 (sin x)^3 + 2 sin x (1 - (sin x)^2)
= 3 sin x - 4 (sin x)^3

cos 3x
= cos(x + 2x)
= cos x cos 2x - sin x sin 2x
= cos x (2 (cos x)^2 - 1) + 2 cos x (sin x)^2
= 2 (cos x)^3 - cos x - 2 cos x (1 - (cos x)^2)
= 4 (cos x)^3 - 3 cos x @ninjasandtigers

Answer 2

Do you understand?

Answer 3

but none of those are in the answer choices
cos x - 4 cos x sin2x

-sin3x + 2 sin x cos x

-sin2x + 2 sin x cos x

2 sin2x cos x - 2 sin x cos x

Answer 4

I would choose the 2nd one.

Answer 5

can you explain why?

Answer 6

Ugh .-. I have to type a lot but I'm just going to say I think it's the 2nd one... So if you don't find my answer helpful you can click (Bump) so someone else can help and if you find it helpful then simply click "Best Response" K? Thanks :P

Answer 7

oh..um ok

Answer 8

the second one wasn't the answer :/ @Jesstho.-.