curl ignore script and style tags while saving

Question

i download pages from the site in loops using curl in the following way:

curl -s "site${n}" -o ./"page${n}".html

is there any way or maybe there is an option in curl to ignore everything between <script>...</script> and <style>...</style> tags while saving page? these parts in the pages are redundant in my case and only consume space.

I can think of something like the following solution so far, but I'm not sure if it's effective:

curl -s "site${n}" | sed ...ignore tags... > ./"page${n}".html