A fun aspect of trig is all the relations and expression that come from adding and subtracting angles inside the unique trig functions! These relations can be super helpful when solving complex trigonometric problems. This is part of the Prelim Maths Extension 1 Syllabus from the topic Trigonometric Functions: Further Trigonometric Identities. In this post, we will explore the sums and differences of angles.
Some relevant equations here are:
- sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
- sin(a-b) = sin(a) cos(b) - cos(a) sin(b)
- cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
- cos(a-b) = cos(a) cos(b) + sin(a) sin(b)
- tan(a+b) = \frac{tan(a) + tan(b)}{1-tan(a)tan(b)}
- tan(a-b) = \frac{tan(a) - tan(b)}{1+tan(a)tan(b)}
Part 1
Part 2
Part 3
