You should really make different threads for different questions, especially when the threads would normally be in different forums...
Anyway, for the trinomials question, for a trinomial , multiply your and values together. Whatever two numbers you pick has to multiply to give this number, and add to give the value.
So for the first...
multiplying the and values gives .
So your two numbers have to multiply to give and add to be . So choose .
Now we break up the middle term using these two values and factorise by grouping.
Try the second one yourself
For the trig questions:
The first one is a quadratic in . So let to give
which you should be able to factorise using the same method I showed you and solve using NFL. Once you have , you know what is, so you should be able to find .
For the second trig question, try converting everything to sines and cosines, using . Everything should fall into place. The Pythagorean Identity will also come in handy.