**What will you learn in this article?**

- Addition and Subtraction of Trigonometric Functions
- Formulae for changing product into sum or differences and vice-versa
- Multiple angles and Submultiple angles along with formulae

##### Previous Article

Before reading this article, do go through trigonometry article 1 and article 2 for a better understanding of the topic.

**Addition and Subtraction of Trigonometric Functions**

There are 7 general formulae that is used in addition and subtraction of trigonometric functions. These formulae are:

- sin (A±B) = sin A cos B ± cos A sin B
- cos (A±B) = cos A cos B ± sin A sin B
- tan (A±B) = (tan A ± tan B) / (1∓tan A tan B)
- cot (A±B) = (cot A cot B ∓ 1)/ (cot B ± cot A)
- sin (A+B) sin (A-B) =A -B =B -A
- cos (A+B) cos (A-B) =A -B =B -A
- tan (A+B+C) = (tan A +tan B +tan C -tan A tan B tan C) / (1-tan A tan B -tan B tan C -tan C tan A)

**Formulae for changing product into sum or difference and vice-versa**

Now, some questions are asked in competitive exams, where you’ll have to find the sum or difference of trigonometric functions when it is given in product form. For this, there are 4 formulae that we can use. They are:

- 2 sin A cos B = sin (A+B) +sin (A-B)
- 2 cos A sin B = sin (A+B) -sin (A-B)
- 2 cos A cos B = cos (A+B) +cos (A-B)
- 2 sin A sin B = cos (A-B) -cos (A+B)

So, these are the formulae to change product into sum or difference. But, sometimes this might be asked in the reverse way. That is, you’ll have to find the product from a given sum or difference between trigonometric functions. To do that, we have another set of 4 formulae. They are:

- sin A + sin B =2 sin (A+B)/2 cos (A-B)/2
- sin A – sin B =2 cos (A+B)/2 sin (A-B)/2
- cos A + cos B =2 cos (A+B)/2 cos (A-B)/2
- cos A – cos B =2 sin (A+B)/2 sin (B-A)/2

**Multiple and Sub-multiple angles**

Multiple angles are basically the angles that we use generally, which are given as a single non fraction unit. For example, sin A is a trigonometric function with multiple angle. On the other hand, Sub-Multiple angles are those which are given in fractional format. For example, sin A/2 is a trigonometric function with sub-multiple angle.

##### Formulae for Multiple Angles

We can define 9 formulae for multiple angles. They are:

##### Formulae for sub-multiple angles

We can define 3 formulae for sub-multiple angles. They are: