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Ierofanga [76]
3 years ago
5

Cos(x + y) + cos(x − y) = 2 cos(x) cos(y)

Mathematics
2 answers:
Andre45 [30]3 years ago
7 0

Answer:

2cos(\frac{x+y+x-y}{2}) cos(\frac{x+y-x+y}{2})

2cos(\frac{2x}{2})cos(\frac{x+y-x+y}{2})

2cos(x)cos(\frac{2y}{2})

2cos(x)cos(y)

Alex17521 [72]3 years ago
6 0
   
\texttt{We use formula: }~~~  \boxed{\cos(x\pm y) = \cos (x) \cos (y) ~\mp ~\sin (x) \sin (y)}\\\\
\cos(x + y) + \cos(x - y) =\\\\
= \underbrace{\cos (x) \cos (y) -\sin (x) \sin (y)}_{\cos(x + y) } +\underbrace{\cos (x) \cos (y) +\sin (x) \sin (y)}_{\cos(x - y)} =\\\\
=\cos (x) \cos (y)+\cos (x) \cos (y)-\sin (x) \sin (y)+\sin (x) \sin (y)=\\\\
=\cos (x) \cos (y)(1+1) + \sin (x) \sin (y)(-1+1) = \\\\
=2\cos (x) \cos (y) + 0\sin (x) \sin (y) = \boxed{\boxed{2\cos (x) \cos (y)}}



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