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Perl - 74 bytes

$~=<>=~$"+$'*2;$_=1-$_*$`/$~--/$~*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

Or, counting command line options as 1 byte each, in 72 bytes:

#!perl -n
$-=/ /+$'*2;$_=1-$_*$`/$---/$-*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

Or, if you'll allow me Perl 5.8, in 65 bytes:

#!perl -p
$.+=$'<</ /;$_=1-$_*$`/$.--/$.*$`for($_=$#='%.8f
',$\)x$';$_*=$`

but why would you.

<> =~ m/ /;          # read one line from stdin, match a space
                     # prematch ($`) is now x, postmatch ($') is now n
($x, $n) = ($`, $'); # reassign, for clarity
$i = 2*$n + 1;       # counting variable (denominators)

for (($s, $c)x$n) {  # iterate over $s and $c, n times each
  # compute the next term of the recursive expression
  # note: inside this loop $_ is not the _value_
  # of $s and $c alternately, it _is_ $s and $c

  $_ = 1 - $_ * $x**2 / $i-- / $i;
}

# formated output
printf("%.8f\n%.8f", $x*$s, $c);

$ echo 5 3 | perl sin-cos.pl
10.20833333
14.54166667

$ echo 9.26 50 | perl sin-cos.pl
0.16403330
-0.98645480

$ echo 6.54 12 | perl sin-cos.pl
0.25398611
0.96714730

$ echo 5 1 | perl sin-cos.pl
5.00000000
1.00000000

Perl - 72 bytes

$~=<>=~$"+$'*2;$_=1-$_*$`/$~--/$~*$`for($,,$;)x$';printf'%f
%f',$`*$,,$;

Or, counting command line options as 1 byte each, in 70 bytes:

#!perl -n
$-=/ /+$'*2;$_=1-$_*$`/$---/$-*$`for($,,$;)x$';printf'%f
%f',$`*$,,$;

Or, if you'll allow me Perl 5.8, in 63 bytes:

#!perl -p
$.+=$'<</ /;$_=1-$_*$`/$.--/$.*$`for($_=$#='%f
',$\)x$';$_*=$`

but why would you.

Edit: Compliance with the new rules. %f rounds to 6 places by default, how convenient!

<> =~ m/ /;          # read one line from stdin, match a space
                     # prematch ($`) is now x, postmatch ($') is now n
($x, $n) = ($`, $'); # reassign, for clarity
$i = 2*$n + 1;       # counting variable (denominators)

for (($s, $c)x$n) {  # iterate over $s and $c, n times each
  # compute the next term of the recursive expression
  # note: inside this loop $_ is not the _value_
  # of $s and $c alternately, it _is_ $s and $c

  $_ = 1 - $_ * $x**2 / $i-- / $i;
}

# formated output
printf("%f\n%f", $x*$s, $c);

$ echo 5 3 | perl sin-cos.pl
10.208333
14.541667

$ echo 8.555 13 | perl sin-cos.pl
0.765431
-0.641092

$ echo 9.26 10 | perl sin-cos.pl
-3.154677
-8.404354

$ echo 6.54 12 | perl sin-cos.pl
0.253986
0.967147

$ echo 5 1 | perl sin-cos.pl
5.000000
1.000000

$ echo 20 20 | perl sin-cos.pl
-5364.411846
-10898.499385

$~=<>=~$"+$'*2;$_=1-$_*$`/$~/--$~*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

#!perl -n
$~=/ /+$'*2;$_=1-$_*$`/$~/--$~*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

#!perl -p
$%=/ /+$'*2;$_=1-$_*$`/$%--/$%*$`for($_=$#='%.8f
',$\)x$';$_*=$`

$_ = <>;             # read one line from stdin
m/ /;                # match a space
                     # prematch ($`) is now x, postmatch ($') is now n
($x, $n) = ($`, $'); # reassign, for clarity
$i = 2*$n + 1;       # counting variable (denominators)

for (($s, $c)x$n) {  # iterate over $s and $c, n times each
  # compute the next term of the recursive expression
  # note: inside this loop $_ is not the _value_
  # of $s and $c alternately, it _is_ $s and $c

  $_ = 1 - $_ * $x**2 / $i / --$i;
}

# formated output
printf("%.8f\n%.8f", $x*$s, $c);

$~=<>=~$"+$'*2;$_=1-$_*$`/$~--/$~*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

#!perl -n
$-=/ /+$'*2;$_=1-$_*$`/$---/$-*$`for($,,$;)x$';printf'%.8f
'x2,$`*$,,$;

#!perl -p
$.+=$'<</ /;$_=1-$_*$`/$.--/$.*$`for($_=$#='%.8f
',$\)x$';$_*=$`

<> =~ m/ /;          # read one line from stdin, match a space
                     # prematch ($`) is now x, postmatch ($') is now n
($x, $n) = ($`, $'); # reassign, for clarity
$i = 2*$n + 1;       # counting variable (denominators)

for (($s, $c)x$n) {  # iterate over $s and $c, n times each
  # compute the next term of the recursive expression
  # note: inside this loop $_ is not the _value_
  # of $s and $c alternately, it _is_ $s and $c

  $_ = 1 - $_ * $x**2 / $i-- / $i;
}

# formated output
printf("%.8f\n%.8f", $x*$s, $c);