Converting Trig (1 Viewer)

[wind]

I hate maths so I'd blame by incompetence on that

Anyways!

I've never figured out how to express say cos6x in terms of cos²x.

Help would be much appreciated!

 

[Estel]

That might have something to do with the fact it wouldn't be asked in 3u.......


and can't be done

 

[gordo]

cos 2x = 2cos^2(x) - 1
therefore cos6x = 2cos^2(3x) - 1

 

[wind]

Thanks a lot!!

 

[Shuter]

I hate maths so I'd blame by incompetence on that

Anyways!

I've never figured out how to express say cos6x in terms of cos²x.

Help would be much appreciated!

cos6x = cos(4x+2x)

= cos4xcos2x - sin4x sin2x
= cos(2x+2x)cos2x - sin(2x+2x) sin2x
= cos2x(cos2xcos2x - sin2x sin2x) - sin2x(sin2x cos2x + sin2x cos2x)
= cos2x cos2x cos2x - sin2x sin2x cos2x - sin2x sin 2x cos2x - sin2x sin 2x cos2x
= cos2x cos2x cos2x - sin2x sin2x sin2x

And I'm not going to finish it.

 

[Estel]

he said cos^2x.
I maintain that cos^2(x)=/cos^2(3x)!

(to gordo)