Returns terms from a different taxonomy using common published posts as search criteria. (Ex: get post tags assigned to all posts in a specific category)

get_terms_by_common_posts.php

<?php
/**
 * Returns terms from a different taxonomy using common published posts as search criteria. 
 * Example: get list of post tags assigned to all posts in a specific category.
 *
 * @param array $ids Array of source term ids.
 * @param string $source Source taxonomy.
 * @param string $target Target taxonomy.
 *
 * @return array
 */
function get_terms_by_common_posts( array $ids = array(), $source = 'category', $target = 'post_tag' ) {
	$ids = array_filter( array_map( 'absint', $ids ) );
	if( !empty( $ids ) ) {
		global $wpdb;
		$ids_sql = join( ', ', array_fill( 0, count( $ids ), '%d' ) );
		// TODO: create the same thing that will support hierarchical taxonomies.
		$sql = "SELECT DISTINCT
			tterms.term_id as id
		FROM
			{$wpdb->posts} as p1
			LEFT JOIN {$wpdb->term_relationships} as r1 ON p1.ID = r1.object_ID
			LEFT JOIN {$wpdb->term_taxonomy} as stermtax ON r1.term_taxonomy_id = stermtax.term_taxonomy_id
			LEFT JOIN {$wpdb->terms} as sterms ON stermtax.term_id = sterms.term_id,

			{$wpdb->posts} as p2
			LEFT JOIN {$wpdb->term_relationships} as r2 ON p2.ID = r2.object_ID
			LEFT JOIN {$wpdb->term_taxonomy} as ttermtax ON r2.term_taxonomy_id = ttermtax.term_taxonomy_id
			LEFT JOIN {$wpdb->terms} as tterms ON ttermtax.term_id = tterms.term_id
		WHERE (
			stermtax.taxonomy = %s
			AND sterms.term_id IN ( {$ids_sql} )
			AND ttermtax.taxonomy = %s
			AND p1.ID = p2.ID
			AND p1.post_status = 'publish'
			AND p2.post_status = 'publish'
		)";
		$args = array_merge(
			array( $sql ),
			array( $source ),
			$ids,
			array( $target )
		);
		$query = call_user_func_array( array( $wpdb, 'prepare' ), $args );
		$results = $wpdb->get_results( $query );
		$terms = empty( $results ) ? array() :  wp_list_pluck( $results, 'id' );
		$terms = apply_filters( 'get_terms_by_common_posts', $terms, $ids, $source, $target );
		return empty( $terms ) ? array() : get_terms( array( 'taxonomy' => $target, 'include' => $terms ) );
	}
	return array();
}

Example of getting all post tags assigned to posts in category id = 1
$tags = get_terms_by_common_posts( array(1), 'category', 'post_tag' );