Can only find one double angle formula of cos(2x).

close all
clear
clc

syms x

expand (cos(2*x))

ans =

2*cos(x)^2 - 1

That is one of the three double angle formulas for cos(2x).

How do I get matlab to show the other two double angle formulas?

Answer 1

[Star Strider]

Experiment with various options to get at least one more identity —

syms x 
f(x) = cos(2*x)

f(x) = 

f1 = expand (f)

f1(x) = 

f2 = rewrite(f, 'exp')

f2(x) = 

f3 = rewrite(f2, 'sin')

f3(x) = 

.

[Jan]

And cos(x)^2 - sin(x)^2 ?

[John D'Errico]

Simple enough, since we can add zero to an identity and have it be still valid...

syms x 
f(x) = cos(2*x);
f1 = expand(f)

f1(x) = 

Just adding one identity to another:

f4 = f1 + 1 - sin(x)^2 -cos(x)^2

f4(x) = 

I don't think MATLAB really cares about how many versions of the same identity it can show, since they are all mathematically identical.

[Kevin]

Wait, sorry but I don't understand what you're doing to get f4(x) = cos(x)^2-sin(x)^2.

[Star Strider]

@John D'Errico — Thank you!

.

[Jan]

@John Ooi: He adds:

0 = 1 - 1 = 1 - (sin(x)^2 + cos(x)^2) = ...
          = 1 - sin(x)^2  - cos(x)^2

@John D'Errico: Yes, Matlab does not care, because all these expressions are equivalent. But I was curious how to bring the symbolic engine to express the different forms. Thanks for showing this.