Remove tagline from the HTML on the home page without plugin?

If first check in your header.php file and check in title tag what is print. if in title tag bloginfo then it’s replace with wp_title(”) because bloginfo is not replace with code.

Header.php

<title><?php wp_title(''); ?></title>

After function.php file put this code:

    function wpdocs_theme_name_wp_title( $title, $sep ) {
    if ( is_feed() ) {
        return $title;
    }

    if (  is_home() || is_front_page() )  {
        return $title;
    }

    global $page, $paged;

    // Add the blog name
    $title .= bloginfo( 'name' );

    // Add a page number if necessary:
    if ( ( $paged >= 2 || $page >= 2 ) && ! is_404() ) {
        $title .= " $sep " . sprintf( __( 'Page %s', '_s' ), max( $paged, $page ) );
    }

    return $title;
}
add_filter( 'wp_title', 'wpdocs_theme_name_wp_title', 10, 2 );

NOTE: your title tag is blank then in tab display your SITE URL.