Why त्रिनयनः & त्रिनेत्रः is not as त्रिणयनः & त्रिणेत्रः?
पूर्वपदात्संज्ञायाम् अगः (८-४-३) is the Paninian rule. If र् or ष् occurs in the first member of (previous word of) a compound and this first member (previous word) does not have ग्, then न् in the second member of the compound is replaced by ण्, if the whole compound refers to a name - is the meaning of this Sutra. खरणसः is the example. Here, in the compound word खरणस, there two members खर+नस. The first member has र् and there is no ग् in it. So in the second member न् in नस is replaced by ण् as the whole compound refers to a name. Hence खरणस is the resultant word.
In the same way, त्रिनयनः and त्रिनेत्रः are also refer to a name (name of Shiva), र् is found in the first member of the compound, there is no ग् in it. So न् in the second member of the compound should be replaced by ण् as per this Sutra and the resultant words should be त्रिणयनः and त्रिणेत्रः. But, here we find त्रिनयनः and त्रिनेत्रः only. Why here न् is not replaced by ण्?
The answer to this question is given like this – There is another Sutra क्षुभ्नादिषु च (८-४-३८). न् is not replaced by ण् in the words listed under क्षुभ्नादि group. But, the problem is we could not find नयनः and नेत्रः under this group. Then how is it not replaced? Here, Patanjali in his Bhashya on this Sutra says that अविहितलक्षणो णत्वप्रतिषेधः क्षुभ्नादिषु द्रष्टव्यः meaning if the instance of this rule “न् is not replaced by ण्” is not found anywhere, then it is to be taken as if it listed under क्षुभ्नादि group. As क्षुभ्नादि is classified as आकृतिगण, we have to infer that such words as listed in that गण.
So, in त्रिनयनः and त्रिनेत्रः, न् is not replaced by ण् as they are treated as listed under क्षुभ्नादि group.