令40°=35°+5°，30°=35°-5°，sin40°+cos30°=sin35°cos5°+cos35°sin5°+cos35°cos5°+sin35°sin5°=（sin35°+cos35°）（sin5°+cos5°）=（sin55°+sin35°）（sin85°+sin5°）=2sin45°cos10°（2sin45°cos40°）=2cos40°cos10°
