How to perform a search inside a specific taxonomy category

try this:
Put this code in your search form:

<form method="get" id="searchform" action="<?php bloginfo('url'); ?>/search">
<?php 
$args = array(
   'public'   => true,
   '_builtin' => false
); 
$output="objects";
$operator="and"; 
$taxonomies = get_taxonomies( $args, $output, $operator ); 
$my_tax_array = array('your_taxonomy_name1','your_taxonomy_name2',); //make array of your taxonomies
echo "<select id='my_select_taxonomy' name="my_select_taxonomy">";
echo "<option value="0">----</option>";
if ( $taxonomies ) {
  foreach ( $taxonomies  as $taxonomy ) {
    if (in_array($taxonomy->name, $my_tax_array)){
        echo "<option value="{$taxonomy->name}">{$taxonomy->label}</option>";
    }
  }
}
echo "</select><br />";
?>
<input type="text" value="" name="search_field" id="search_field" />
<input type="submit" id="searchsubmit" value="Search" />

And in your search page this:

<?php

$search_field = $_GET['search_field'];
$my_select_taxonomy = $_GET['my_select_taxonomy'];

$args = array(
'post_type' => 'post',
'tax_query' => array(
    array(
        'taxonomy' => $my_select_taxonomy,
        'field' => 'slug',
        'terms' => $search_field,
    )
)
);
$query = new WP_Query( $args );

?>

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