This is a thread for complex number problems in applied mathematics.
You can see attachment for the question.
What help do you need? What do you have so far? For the first one, I would start with multiplying out by $\displaystyle 2(1-\cos \theta)$ and see what you get (consider the sum or difference of angles formula for cosine).
For the second problem, again, I would start with the difference of angles formula for cosine.