knowing that: cos(x)=Σ_(n=1) ^∞ (((−1)^n x^(2n) )/((2n)!)) sin(x)=Σ_(n=1) ^∞ (((−1)^n x^(2n+1) )/((2n +1)!)) prof that: cos(x+y)= cos(x)cos(y)−sin(x)sin(y)


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Question Number 58358 by Mahmoud A.R last updated on 22/Apr/19

$k n o w i n g t h a t :$ $c o s (x) = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n}}{(2 n)!}$ $s i n (x) = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n + 1}}{(2 n + 1)!}$ $p r o f t h a t : c o s (x + y) = c o s (x) c o s (y) - s i n (x) s i n (y)$
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