Trigonometric Functions (Problem Solving Approach) by A. Panchishkin and E. Shavgulidze.

The book has some interesting things, for example it introduces the trigonometric functions as a feature of a trigonometric circle instead of a right-angled triangle as many books do. Also the second chapter (Identical Transformations of Trigonometric Expressions) will help you understand many combination formulae (which we learn by heart in many cases without understanding). Chapter 4 (Investigating Trigonometric Functions) treats the trigonometric functions graphically and analyzes the meaning of graphs, also with help of their derivatives.
LINK1
https://archive.org/details/TrigonometricFunctions-ProblemSolvingApproach
LINK2
http://mirtitles.org/2012/07/04/trigonometric-functions-problem-solving-approach/