The "Tripurantaka" form of Shiva is prominently depicted in the mural paintings of:

The correct option is Brihadeswara Temple.

Explanation

Indian mural paintings have a rich tradition spanning from the ancient caves of Ajanta to the medieval temples of South India. The themes of these paintings vary significantly based on the religious patronage (Buddhist, Jain, or Hindu) and the dynastic style (Gupta, Chalukya, Pallava, Chola, etc.).

Detailed Analysis:

• Brihadeswara Temple: Brihadeswara Temple (Correct)
  The Brihadeswara Temple at Thanjavur, built by the Chola emperor Raja Raja Chola I, houses some of the finest examples of Chola fresco paintings. A prominent masterpiece within the circumambulatory passage (pradakshinapatha) of the vimana is the massive depiction of Shiva as Tripurantaka (the destroyer of the three cities of demons). In this mural, Shiva is depicted as a warrior with eight arms, riding a chariot driven by Brahma, demonstrating the martial and artistic grandeur of the Chola period.
• Badami Caves: Badami Caves (Incorrect)
  The Badami Caves (Karnataka) represent the earliest surviving Brahmanical (Hindu) mural paintings, patronized by the Chalukyas. The most famous surviving painting here depicts the palace scene of Indra and his retinue. While Shiva is sculpted in the caves, the defining mural is not the Tripurantaka form.
• Sittanavasal: Sittanavasal (Incorrect)
  Sittanavasal (Tamil Nadu) is a rock-cut cave temple associated with Jainism (Pandya/Pallava period). The paintings here are renowned for the "Lotus Pond" scene and figures of Tirthankaras, not Hindu deities like Shiva.
• Ajanta: Ajanta (Incorrect)
  The murals at Ajanta are exclusively Buddhist in theme, depicting Jataka tales and the life of Buddha. They do not feature Hindu deities like Shiva.

Key Takeaway:

The Tripurantaka form of Shiva is a signature theme in Chola art, famously depicted in the mural paintings of the Brihadeswara Temple in Thanjavur.