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

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Kevin il 10 Set 2021
Commentato: Jan il 10 Set 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?
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### Risposta accettata

Star Strider il 10 Set 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) =
.
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Jan il 10 Set 2021
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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