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

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Kevin
Kevin on 10 Sep 2021
Commented: Jan on 10 Sep 2021
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?

Accepted Answer

Star Strider
Star Strider on 10 Sep 2021
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) = 
.
  5 Comments
Jan
Jan on 10 Sep 2021
@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.

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