You need to know the double angle formulas for that. Very trivial if you know them. Also don't forget to remember them by heart also the triple angle one's as well. And don't just remember them like a parrot, understand their proofs, so that when in future you need let's say four or five angle formulas you know how to find them.
Also remember you can manipulate the formulas for your convenience. And good mathematician is a master manipulator.
Like : Sin2A = 2SinACosA can also be remembered as SinA= 2SinA/2CosA/2.
Now the real question is how you know become a master in manipulation.
The answer is PRACTICE and Lots of it.
Let me give you my example:
When I was in 1st year I studied "Solving Differential Equations". There were so many methods and the procedure was lengthy but than I also read about "Exact method of solving DEs" and I found it to be very simple but very tough at the same time. I perfected it by practicing a lot. And now I can solve most of the entry level ODEs without pen and paper.
> Good at math
> Practice
Pick One