Seamless way to check if user likes page

Of course you can! As mentioned in the documentation, Facebook will send you some extra details in the signed_request:

When a user navigates to the Facebook
Page, they will see your Page Tab
added in the next available tab
position. Broadly, a Page Tab is
loaded in exactly the same way as a
Canvas Page. When a user selects your
Page Tab, you will received the
signed_request parameter with one
additional parameter, page. This
parameter contains a JSON object with
an id (the page id of the current
page), admin (if the user is a admin
of the page), and liked (if the user
has liked the page). As with a Canvas
Page, you will not receive all the
user information accessible to your
app in the signed_request until the
user authorizes your app.

The code taken from my tutorial should be something like:

<?php
if(empty($_REQUEST["signed_request"])) {
    // no signed request where found which means
    // 1- this page was not accessed through a Facebook page tab
    // 2- a redirection was made, so the request is lost
    echo "signed_request was not found!";
} else {
    $app_secret = "APP_SECRET";
    $data = parse_signed_request($_REQUEST["signed_request"], $app_secret);
    if (empty($data["page"]["liked"])) {
        echo "You are not a fan!";
    } else {
        echo "Welcome back fan!";
    }
}

function parse_signed_request($signed_request, $secret) {
    list($encoded_sig, $payload) = explode('.', $signed_request, 2); 

    // decode the data
    $sig = base64_url_decode($encoded_sig);
    $data = json_decode(base64_url_decode($payload), true);

    if (strtoupper($data['algorithm']) !== 'HMAC-SHA256') {
        error_log('Unknown algorithm. Expected HMAC-SHA256');
        return null;
    }

    // check sig
    $expected_sig = hash_hmac('sha256', $payload, $secret, $raw = true);
    if ($sig !== $expected_sig) {
        error_log('Bad Signed JSON signature!');
        return null;
    }

    return $data;
}

function base64_url_decode($input) {
    return base64_decode(strtr($input, '-_', '+/'));
}
?>

UPDATED CODE: While the previous code would work. I wasn’t checking the validity of the request. This means someone could tamper the request and send you false information (like setting the admin to true!). Code has been updated, following the signed_request documentation approach.