From Ayodhya Kanda - Book Of Ayodhya Chapter [Sarga] 25:
smR^itir dhR^itiH ca dharmaH ca paantu tvaam putra sarvataH | skandaH ca bhagavaan devaH somaH ca sabR^ihaspatiH || 2-25-11 sapta R^iSayo naaradaH ca te tvaam rakSantu sarvataH |
"May Veda, the Smriti texts taken as one body, the resolution and the piety protect you, my son! May lord Skanda (the younger son of Lord Siva)and the moon god along with the sage Brihaspati(the preceptor of gods), the well known seven sages as well as Sage Narada guard you on all sides."
sarva loka prabhur brahmaa bhuuta bhartaa tathaa R^iSayaH || 2-25-25 ye ca sheSaaH suraaH te tvaam rakSantu vana vaasinam |
"Let Siva, the lord of all spheres, Brahma, the lord of creation, Vishnu, the nourisher of beings, the sages and the rest of the celestials may protect you dwelling in the forest."
mayaa arcitaa deva gaNaaH shiva aadayo | maharSayo bhuuta mahaa asura uragaaH | abhiprayaatasya vanam ciraaya te| hitaani kaankSantu dishaH ca raaghava || 2-25-45
"Oh, Rama! Worshipped by me, let the hosts of gods headed by Siva, the Supreme Being, the great sages, spirits, the chief of evil spirits, the celestial serpents and the (four)quarters wish well of you, who is setting forth to forest, "
Here we can see that his mother clearly worshipped Shiva. What is the basis to say Rama didn't worship Shiva?
"See this island, located in the middle of the ocean, where my troops were stationed. At this place, the lord Shiva (the supreme deity) formerly bestowed his grace on me."
—Quote taken from Valmiki Ramayana, Yuddha Kanda, Sarga 123, Verse 19
This quote is taken from answer given here(it's not my finding)— https://hinduism.stackexchange.com/questions/10945/did-lord-rama-really-worship-lord-shiva
– Fierce lord Feb 13 '18 at 07:21