Hello!

Basically I am stuck... been pulling my hair out trying to simplify this and come out with a simple expression!

Also not sure what area of the forum to put this in, but seeing as there is nothing too complicated and its all algebra i think this is the right place.

Heres the problem:

Two balls are thrown at angles , , at velocity one after the other such that they collide at point B in mid air, determine the time between the throws (analytically).

Heres what i have done so far:

Resolving horizontally gives:

and

Resolving Vertically gives:

Sub in the expression for to find the eqn in terms of then my plan is to simplify and do the same for until finally i can do:

where is the answer to the problem.

Okay, so heres where i am stuck:

Trying to simplify the eqn. for , im not sure exactly how to do this:

I have a similar expression for .

How do i simplify that?

EDIT: I am guessing there is a trig identity for bottom part which can be written:

but i cant remember it!

EDIT 2: Perhaps there isnt, so i tried simplifying and got this:

Is that okay?