is some between and with
Furthermore, with and a positive number, we conclude that is between 0 and .
We want to find and we already know . So if we find , then we can ue the double angle formula for sine.
You've probably done this kind of problem many times by now. is in the first quadrant and , find .
Use your favorite method -- draw a triangle, or a unit circle, or an angle in standard position, or skip the picture and use (recall that our is in Quadrant 1, so its cosine is positive.)
All of the above is really explanation of our thought process.
All we really need to write is something like:
Let , then and
So, putting it all together we get:
Not exactly what you’re looking for?