Why doesn’t Shiva worship anybody where as Vishnu worships him in all his incarnations?
Though the god is one, when we see in terms of Generation, Operation, Destruction these are taken care by Brahma, Vishnu and Shiva respectively. Since Vishnu is responsible for execution, it is He who descends to take care of the creation. This may be killing the demons or establishing dharma or to spread knowledge or to fulfill desire of a devotee. No one can understand Him, so He shows how to worship Him for different purposes. Also Vishnu worships Shiva symbolically to say both are same.
‘Sivasya hridayam vishnur-vishnoscha hridayam sivah’ — Vishnu is the heart of Shiva and likewise Shiva is the heart of Vishnu."
They both meditate upon one another all the time! A good discussion on this is here
In other perspective Vishnu has taken Rajas nature and Shiva has taken Sattva. Rajas is full of desires and action and hence He worships Shiva to fulfill the desires, this way He shows how to worship the god whereas Shiva is satvik, He is self realized and self sufficient and hence He doesn't appear to worship anyone externally.
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