Can addition formula be applied to more than 2 sums?

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lax1113
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Homework Statement



Not an actual problem, but to help solve my homework, would cos(A+B+C)=
CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny)

I was unsure if this can be applied to multiple digits or only 2.



I know I could plug in numbers to test, but I was wondering about the logic behind this.
 

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lax1113 said:

Homework Statement



Not an actual problem, but to help solve my homework, would cos(A+B+C)=
CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny)

I was unsure if this can be applied to multiple digits or only 2.



I know I could plug in numbers to test, but I was wondering about the logic behind this.
No, that's not it.

Expand cos((A+B) + C) first, and then expand the factors with cos(A+B) and sin(A+B).
 
I see.

So Cos(A+B+C) =

cos((CosAcosB-sinAsinB)+C)

then use the value from the first portion in another addition formula with C?