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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:

\[\large Sin(\alpha – \beta )=Sin\,\alpha\;Cos\,\beta-Cos\,\alpha\;Sin\,\beta\]

Cos Subtracting formula:

\[\large Cos(\alpha – \beta )=Cos\,\alpha\;Cos\,\beta-Sin\,\alpha\;Sin\,\beta\]

Tan Subtracting formula:

$\LARGE Tan(\alpha – \beta )=\frac{Tan\,\alpha\;Tan\,\beta}{1+Tan\,\alpha\;Tan\,\beta}$ 

Solved example

Question: What is the value of cos 30$^{\circ}$?

Solution:

Given,
Cos 30$^{\circ}$
It can be written as Cos 60$^{\circ}$ – Cos 30$^{\circ}$

As we already know the value of 60$^{\circ}$ and Cos 30$^{\circ}$, it is going to be easy for us to solve Cos 30$^{\circ}$.

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

$=\frac{1}{2}\times \frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}\times \frac{1}{2}$

$=\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}$

= 0.75

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