For the second problem, note that , so we have
Multiply out the RHS and use , then solve for sin(x).
You will get
Note that there will be four solutions to this.
Wow. Lots of posting going on in this thread!
The second problem is:
This is not an identity to prove, but an equation to solve.
Using the double-angle identity for sine provided by topsquark, we have:
You will find 4 solutions on the interval . If you are not restricted to an interval, then you will have an infinite number of solutions, which is easily expressed as the integral multiple of an angle.