Trig Identities - How do I identify

During the past few years of teaching trig, I have always had students struggle significantly with the trig identity chapter. Every semester I try to tweak the way I teach the material and the practice the students receive but I still have students that just don't grasp the material. Fall 2013 I decided to try extending my lecture days by one class and moving the exam. In doing this I was hoping that more time would lead to better success. It still did not make a significant difference.  Thus, this semester I decided to make even bigger changes. I still extended the time we covered the material, but I gave many more practice examples for the students to do in class, in their groups. The take home I have given before but I stressed to them the importance of identifying the pieces of the problem and what they needed to look for in proving both sides. The take home questions are attached and students are not to receive any outside help but I give it as a take home to allow for more time and hopefully quality work. My results from Fall 2013 before more changes was 70% passed and this spring was 90% passed. I will look again in the fall to see if my results hold.