simplify cos (x+y) + cos (x-y)

[sayyadina]

So, cos (x+y)= cos(x)cos(y) - sin(x)sin(y). And cos(x-y)= cos(x)cos(y) + sin(x)sin(y).

{cos(x)cos(y) - sin(x)sin(y)} + {cos(x)cos(y) + sin(x)sin(y)}

The -sin(x)sin(y) and + sin(x)sin(y) cancel to leave

{cos(x)cos(y)} + {cos(x)cos(y)}

cos(x) + cos(x) = 2cos(x)

cos(y) + cos(y) = 2cos(y)

So, the answer is 2cos(x)2cos(y).....right? Or am I missing something?

 

[pka]

So, cos (x+y)= cos(x)cos(y) - sin(x)sin(y). And cos(x-y)= cos(x)cos(y) + sin(x)sin(y).

{cos(x)cos(y) - sin(x)sin(y)} + {cos(x)cos(y) + sin(x)sin(y)}

The -sin(x)sin(y) and + sin(x)sin(y) cancel to leave

{cos(x)cos(y)} + {cos(x)cos(y)} CORRECT to this point.

$\displaystyle \cos(x)\cos(y) + \cos(x)\cos(y)=2\cos(x)\cos(y)$