# Subtraction Formulas

With trigonometry values, and subtraction formulas it is going to be easy to solve the complicated expression or finding an exact value. When the difference of two angles are needed, then subtraction formula can be used for the exact values.

The Sin subtraction formula of trigonometry is given as:

sin(A âˆ’ B) = sin A cos B âˆ’ cos A sin B

Cos Subtracting formula:

cos(A âˆ’ B) = cos A cos B + sin A sin B

Tan Subtracting formula:

tan(A âˆ’ B) = (tan A âˆ’ tan B) / (1 + tan A tan B)

### Solved example

Question:Â What is the value of cos 30

$$\begin{array}{l}^{\circ}\end{array}$$
?

Solution:

Given,
CosÂ 30

$$\begin{array}{l}^{\circ}\end{array}$$

It can be written as Cos 60
$$\begin{array}{l}^{\circ}\end{array}$$
– CosÂ 30
$$\begin{array}{l}^{\circ}\end{array}$$

As we already know the value of 60

$$\begin{array}{l}^{\circ}\end{array}$$
and CosÂ 30
$$\begin{array}{l}^{\circ}\end{array}$$
, it is going to be easy for us to solve CosÂ 30
$$\begin{array}{l}^{\circ}\end{array}$$
.

$$\begin{array}{l}Cos(60^{\circ}-30^{\circ})=Cos\,60^{\circ} \times Cos\,30^{\circ}+Sin\,60^{\circ} \times Sin\,30^{\circ}\end{array}$$

$$\begin{array}{l}=\frac{1}{2}\times \frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}\times \frac{1}{2}\end{array}$$

$$\begin{array}{l}=\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}\end{array}$$

=Â 0.866