Question

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

Answer 1

`=sqrt3 /2 cos x - 1/2 sinx - sqrt3 / 2 sinx - 1/2 cos x`

Explanation:

Use the formulas: `cos(A+B)=cosAcosB-sinAsinB` and
`sin(A+B)=sinAcosB+cosAsinB`

`cos(x+pi/6)-sin(x+pi/6)=[cosxcos(pi/6)-sinx sin (pi/6)]-[sinx cos(pi/6)+cos x sin (pi/6)]`

`=[cosx (sqrt3 /2)-sinx (1/2)]-[sinx (sqrt3 /2)+cos x sin(pi/6)]`

`=sqrt3 /2 cos x - 1/2 sinx - sqrt3 / 2 sinx - 1/2 cos x`