# How to simplify an iterated trigonometric expression

• Leo Liu
Leo Liu
Homework Statement
.
Relevant Equations
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eg ##\cos (\sin x)##
Asking this question out of curiosity.

Mentor
Homework Statement:: .
Relevant Equations:: .

eg ##\cos (\sin x)##
Asking this question out of curiosity.
I don't see how you're going to be able to get anything simpler than that.

• Keith_McClary
Homework Helper
Gold Member
Typically this can only be done with the partial sums of the Taylor series of the functions. There are a variety of ways to calculate a partial sum of the composition, including matrix multiplication.

• Leo Liu
Homework Helper
Gold Member
If you are interested about the Fourier series of cos(cos x) or cos (sin x) I think they are related to the Bessel functions.

• Leo Liu
Leo Liu
If you are interested about the Fourier series of cos(cos x) or cos (sin x) I think they are related to the Bessel functions.
Thank you this is the best answer I got :D

• Delta2
Gold Member
Or maybe you want something like :

##Cos^2(sinx)+ Sin^2(sinx)=1##

So that ##Cos(sinx)=\sqrt {1-Sin^2(sinx)}##?

• Leo Liu
Mentor
Or maybe you want something like :

##Cos^2(sinx)+ Sin^2(sinx)=1##

So that ##Cos(sinx)=\sqrt {1-Sin^2(sinx)}##?
I thought of something like this, as well as a Taylor or Maclaurin series, but none of these seemed like they would serve to simplify the given expression.

• Leo Liu, FactChecker and WWGD