Mathematical proof is one of the topics that students find very difficult. Many of them assume what they are trying to prove, end up with a true statement and then think they have proved the result. Studying truth tables, particularly the implication operator may well help. See Logical Operations and Truth Tables
On a mathematics forum a student wanted to use its facilities (provided by LatexRender of course 😎 ) to help a friend show how to prove
This is the original ‘proof’ they gave. Although they have now changed it I get the impression that I failed to convince them of the faulty logic; how would you explain what is wrong?
For this problem you need to know the addition formulas:
Using these formulas in the problem we can turn it into:
Then we use the fact that and
This changes it to:
Here we cancelled out the terms that equals zero and then adding together what we have we end up with: