What's the difference in use?
.
Let's see.
I'm happy to try to answer. - ok
I'm glad to try to answer. - nope strange
I'm glad to be asked to answer. - ok - past tense - ok
I'm happy to be asked to answer. - ok - only works if future.
Today, I'm glad - nope, strange
Today, I'm happy. - ok
Today, I'm glad that it's not raining. - fine
Today, I'm happy that it's not raining. - fine
Glad to finally meet you. -ok
Glad to meet you. - sort of ok
Happy to meet you. - ok
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Glad seems to be more often used for a result, a reaction, not future, or anticipation.
Happy can it seems be used more easily for an impression for anticipation.
Perhaps someone has made up complicated, technical rules to decribe this: what thee are actually used for. Might be easier to just get familiar with the ones that are used till they become natural for you to use.
Happy to try to help.
If it helped, the I'm glad to be of service.