Basically, write \cos 4x as a polynomial in \sin x. I've

Kaspaueru2 2021-12-31 Answered
Basically, write cos4x as a polynomial in sinx.
I've tried the double angles theorem and cos2x=cos2xsin2x. I'm still having trouble right now though.
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Expert Answer

rodclassique4r
Answered 2022-01-01 Author has 37 answers
cos4x=12sin22x
=12(1cos22x)
=12(1(12sin2x)2)
=12(4sin2x4sin4x)
=18sin2x+8sin4x
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scomparve5j
Answered 2022-01-02 Author has 38 answers
If you prefer we can use complex numbers
Let z=cosx+isinx. Using de Moivres
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Vasquez
Answered 2022-01-08 Author has 460 answers

Double angle theorem once:
cos4x=cos22x+sin22x
Double angle theorem twice:
=(cos2xsin2x)2+(2sinxcosx)2)
Expand chicken soup and rice:
=cos4x2cos2xsin2x+sin4x+4sin2xcos2x)
To get it entirely in terms of sinkx replace cos2x with 1sin2x (keeping in mind cos4x=(cos2x)2)
=(1sin2x)22(1sin2x)sin2x+sin4x+4sin2x(1sin2x)

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