Question

How do you simplify `Cos(x+pi/6)-sin(x+pi/6)`?

Answer 1

`=sqrt3/2 cosx-1/2 sinx-sqrt3/2sinx-1/2 cosx`

Explanation:

Use Properties:
`cos(A+B)=cosAcosB-sinAsinB`
`A=x,B=pi/6`

`sin(A+B)=sinAcosB+cosAsinB`
`A=x,B=pi/6`

`cos(x+pi/6)-sin(x+pi/6)=cosxcos(pi/6)-sinxsin(pi/6)-[sinxcos(pi/6)+cosxsin(pi/6)]`

`=cosxcos(pi/6)-sinxsin(pi/6)-sinxcos(pi/6)-cosxsin(pi/6)]`

`=sqrt3/2 cosx-1/2 sinx-sqrt3/2sinx-1/2 cosx`