たしかに＝　Certainly (used when you agree with somebody) もちろん＝　Of course (used to strongly agree with somebody, much stronger and definite) can use mochiron by itself too, もちろん！！　of course!!! Maybe you can for tashikani too but it's not as commonly used by itself, it's like "I certainly agree with what you said, but ___ (and then say a different view" You can do the same with mochiron too though so they are similar, but just mochiron is stronger overall.

2/2 もちろんcan be used when you begin a talk. ○teacher: にほんごの　じゅぎょうには　もちろん　きょうかしょが　ひつようです。Of course you need a textbook for Japanese classes. ×teacher: にほんごの　じゅぎょうには　たしかに　きょうかしょが　ひつようです。You surely need a textbook for Japanese classes. student: にほんごの　じゅぎょうには きょうかしょが　ひつようですよね。We need a textbook for Japanese classes, don't we? ○teacher: はい、たしかに　きょうかしょが　ひつようです。Yes, you surely need a textbook. ○teacher: はい、もちろん　きょうかしょが　ひつようです。Of course you need a textbook. もちろんcan not be used as a word to confirm. ambulance crew: これがアールエイチマイナスの血液です。This is the blood of Rh－. ○doctor: はい、たしかに（受け取りました）。Yes, (I) surely (received it). ×doctor: はい、もちろん（受け取りました）。Yes, of course (I) (received it). もちろんcan be used as a predicate with だ／です. ○にほんごの　じゅぎょうに　きょうかしょが　ひつようなのは　もちろんです。A textbook being necessary for Japanese classes of course. ×にほんごの　じゅぎょうに　きょうかしょが　ひつようなのは　たしかにです。 ※ ○にほんごの　じゅぎょうに　きょうかしょが　ひつようなのは　たしかです。It is sure that you need a textbook for Japanese classes.

※My answer is too long for the box for answering. It's different from the box for correcting. So I divide it into two and send it. 1/2 ○correct △strange a little ×incorrect たしかにsurely / I'm sure / certainly / I'm confident with it because I confirmed it. もちろん（×もっちろ）of course / needless to say / as a common sense policeman: あなたは　ほんとうに　その　おとを　ききましたか。Did you surely hear that sound? ○informer: はい、たしかに ききました。Yes, I surely heard it ( I can remember the situation at that time). △informer: はい、もちろん ききました。Yes, of course I heard it ( because it was so loud / that's why I informed to the police). ○わすれたんですか。わたしは たしかに　あなたに　いいましたよね。Did you forget it? I surely said to you, didn't I ? ×わすれたんですか。わたしは　もちろん　あなたに　いいましたよね。Did you forget it? Of course, I said to you, didn't I ?