You should use wp_enqueue_style() to add stylesheets to your template.
function add_stylesheets() {
wp_register_style( 'style', get_stylesheet_uri() );
wp_register_style( 'bxslider', get_template_directory_uri() . 'jquery.bxslider.css' );
wp_register_style( 'responsive', get_template_directory_uri() . 'responsive.css' );
wp_enqueue_style('style'); // enqueue style.css everywhere
## if( ! is_page_template('landingpage.php') ) // enqueue style.css everywhere except if the page template is landingpage.php
## wp_enqueue_style('style');
## if( ! is_page(ID) ) // enqueue style.css everywhere except page id = ID
## wp_enqueue_style('style');
## if( is_home() || is_front_page() ) // enqueue style.css in homepage only
## wp_enqueue_style('style');
wp_enqueue_style('bxslider');
wp_enqueue_setyle('responsive');
}
add_action( 'wp_enqueue_scripts', 'add_stylesheets' );
codeinstead of a snapshot of code.