transform cos 38x to functions of 19x

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transform cos 38x to functions of 19x

Mathematics
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have you heard of the trig identy cos(a+b)=cos(a)cos(b)+sin(a)sin(b)? because cos(38x) can be the same as cos(19x+19x) and so a=19x and b=19x
I Have not heard of that but it makes sense to me. Would that also work to make it a function of 76x?
\[cos(2x)=1-sin^2(x)\]

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so \[cos(76x)=1-sin^2(38x)\]
btw calcstud shows how to derive the formula i wrote.
thank you!

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