Question

Rewrite with only sin x and cos x.

cos 3x

Answer 1

@hartnn

Answer 2

hmm let me think

Answer 3

help me @AlexandervonHumboldt2

Answer 4

maybe write it as cos(2x + x) :-
cos(2x + x) = cos2x cos - sin2x sinx

- not sure - now we have sines involved

Answer 5

oh - thats ok lol

Answer 6

now we can use cos2x = 2cos^2x - 1
and sin2x = 2 sinx cosx

Answer 7

Hmmmmm...... Would that be all?

Answer 8

well substitute for cos 2x and sin 2x and you'll have your answer

Answer 9

cos3x = cos(2x + x) = (2 cos^2x - 1) cos - 2 sinx cos x cos x

= 2 cos^3 x - cos x - 2 sinx cos^2 x

Answer 10

Here are two equations you should memorize, they let you reduce angles down. So start out with cos(x+2x) and then use the formulas again to get rid of the sin(2x) and cos(2x) that pop up. \[\Large \sin(x+y)=\sin x \cos y + \sin y \cos x\\ \Large \cos(x+y)=\cos x \cos y - \sin x \sin y\]

Answer 11

If you have time, there's actually a very simple way of deriving these equations.

Answer 12

Ok, so using that formula I come up with \(cos(x+2x)=cosx~cos2x-sinx~sin2x\)