- #1

- 166

- 2

## Homework Statement

The two vectors

**a**and

**b**lie in the

*xy*plane and make angles

*α*and

*β*with the

*x*axis.

a)By evaluating

**a**•

**b**in two ways (Namely

**a**•

**b**= abcos(θ) and

**a**•

**b**= a1b1+a2b2) prove the well-known trig identity

cos(

*α*-

*β*)=cos(

*α*)cos(

*β*)+sin(

*α*)sin(

*β*)

b)By similarly evaluating

**a**X

**b**prove that

sin(

*α*-

*β*) = sin(

*α*)cos(

*β*) - cos(

*α*)sin(

*β*)

c)Now let vector

**a**make an angle -α with the

*x*axis and find a similar expression for

cos(

*α*+

*β*)

## Homework Equations

**a**•

**b**= abcos(θ)

**a**•

**b**= a1b1+a2b2

## The Attempt at a Solution

I drew the vectors

**a**and

**b**with their appropriate angles to the x-axis... The angle between the vectors is (α-β) so I have

**a**•

**b**= abcos(α-β) but I have no idea how to relate this to the trig identities!