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When meeting someone and you are glad to see them I have learned that one phrase that can be used is: "Я радa видеть вас"
When you want to respond to that and tell that you are also happy to see them would: "Я также рад видеть вас" be a appropriate response?
There's a single word used quite often in such cases: "взаимно". That words is used when you want to express that you share the same feelings with person after he or she expressed that feelings. It could be used both for positive and negative sentiments. For instance:
Пётр: Как же я тебя ненавижу!
Василий: Знаешь, взаимно.
As of your phrase "я так же рад видеть вас" (notice that "так же" in this case is written separately) - it is a valid but slightly non-colloquial form. It sounds a bit pathetic. Something like "и я тоже очень рад" sounds more natural.
