beleuchten
to illuminate
To shine light on something or someone in order to make it bright and visible.
Die Bühne wurde von mehreren Scheinwerfern hell beleuchtet.
The stage was brightly illuminated by several spotlights.

to illuminate / examine
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to illuminate
To shine light on something or someone in order to make it bright and visible.
Die Bühne wurde von mehreren Scheinwerfern hell beleuchtet.
The stage was brightly illuminated by several spotlights.

The verb 'beleuchten' is inseparable with the prefix 'be-'. So the prefix always stays connected to the verb, even in the past participle ('beleuchtet'). It makes the verb 'leuchten' (to shine) transitive, so that it requires a direct object.
Ein Strahler beleuchtet das Kunstwerk.
A spotlight illuminates the artwork.
The figurative meaning is derived directly from the literal one. Just as you shine light on an object with a lamp to make it visible, you can also shed 'light' on an abstract topic to make it easier to understand.
Der Experte soll in seinem Vortrag die wirtschaftlichen Hintergründe beleuchten.
The expert is supposed to examine the economic background in his lecture.
In the literal sense, 'beleuchten' is often used for places or objects. Typical combinations are: 'eine Straße beleuchten' (to illuminate a street), 'ein Gebäude beleuchten' (to illuminate a building), 'eine Szene beleuchten' (to light a scene), or 'ein Gesicht beleuchten' (to illuminate a face).
Die Stadt hat beschlossen, die Brücke nachts farbig zu beleuchten.
The city has decided to illuminate the bridge in color at night.
In the figurative, analytical meaning, 'beleuchten' is combined with abstract nouns. Common phrases are: 'ein Thema beleuchten' (to examine a topic), 'einen Aspekt beleuchten' (to examine an aspect), 'ein Problem beleuchten' (to examine a problem), or 'die Hintergründe beleuchten' (to examine the background).
Der Artikel beleuchtet das Thema von einer ganz neuen Seite.
The article examines the topic from a completely new angle.
to throw
'Licht werfen auf' (to shed light on) and 'beleuchten' can both mean that a topic becomes clearer. Both words use an image from the area of light. 'Licht auf etwas werfen' fits when new information helps you understand something unclear. 'beleuchten' is used more when you examine a topic in more detail or explain it from a particular angle. Learners may confuse the words because they can seem similar in texts about problems, questions, or reports. In practical terms: new clues 'werfen Licht auf' something; a report or analysis 'beleuchtet' a topic.

In ihrem Vortrag beleuchtet meine Schwester die Folgen des Klimawandels.
In her talk, my sister examines the consequences of climate change.
Die neuen E-Mails werfen Licht auf den Fehler im Projekt.
The new emails shed light on the mistake in the project.