Who among the following has the credit to invent and create a new style of 'Bharatanatyam'?

Rukmini Devi Arundale 

The correct answer is Option (3) - Rukmini Devi Arundale 

Rukmini Devi Arundale, an Indian classical dancer, is credited with revitalizing and popularizing Bharatanatyam, a traditional Indian dance form. In the 1930s, Rukmini Devi Arundale founded Kalakshetra, an academy of dance and music, in Chennai, Tamil Nadu. Under her guidance, Bharatanatyam was reimagined as a refined and dignified art form, stripped of its former associations with temple dancing. She introduced changes in costume, choreography, and presentation, infusing Bharatanatyam with a sense of grace, elegance, and spirituality.