# How will you prove the trigonometric formula #cos(A+B)=cosAcosB-sinAsinB# by using formula of cross product of two vectors ?

##### 2 Answers

I could prove it using the dot product of vectors.

#### Explanation:

Let

The unit vectors can be written in Cartesian form as

To prove

We know that dot product of two vectors is

Inserting our unit vectors in the above;

Using equation (1)

LHS

From property of dot product we know that only terms containing

Equating LHS with RHS we obtain

As follows

#### Explanation:

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Let us consider two **unit** vectors in X-Y plane as follows :

#hata-># inclined with positive direction of X-axis at angles**A**# hat b-># inclined with positive direction of X-axis at angles**90-B**, where# 90-B>A# - Angle between these two vectors becomes

#theta=90-B-A=90-(A+B)# ,

Now

Applying Properties of unit vectos

and

Also inserting

Finally we get

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**Sin(A+B) =SinA CosB + CosASinB ** formula can also be obtained

by taking **scalar product** of

Now

Applying Properties of unit vectos

and

Also inserting

Finally we get